Data update
This commit is contained in:
Ingy döt Net
parent
5150844a7d
commit
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7735 changed files with 38060 additions and 199180 deletions
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@ -1,205 +0,0 @@
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pragma Ada_2022;
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with Ada.Text_IO;
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with Ada.Numerics; use Ada.Numerics;
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with Ada.Numerics.Long_Elementary_Functions;
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use Ada.Numerics.Long_Elementary_Functions;
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with Ada.Strings; use Ada.Strings;
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with Ada.Strings.Fixed; use Ada.Strings.Fixed;
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with Prime_Numbers;
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procedure Achilles_Numbers is
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package Long_Integer_Prime_Numbers is new Prime_Numbers
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(Integer, 0, 1, 2);
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use Long_Integer_Prime_Numbers;
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-- A powerful number N is such that for every primer factor P of it
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-- P^2 also divides N
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-- Is_Powerful function decomposes the given number N in its prime factors
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-- and then it checks if each factor squared is a divisor of N
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function Is_Powerful (Number : Natural) return Boolean is
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List : constant Number_List := Decompose (Integer (Number));
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begin
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for Index in List'Range loop
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declare
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N : constant Long_Long_Integer := Long_Long_Integer (Number);
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F : constant Long_Long_Integer := Long_Long_Integer (List (Index));
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begin
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if N mod (F * F) /= 0 then
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return False;
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end if;
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end;
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end loop;
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return True;
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end Is_Powerful;
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-- The Is_Power function checks if a given number N can be written
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-- as a power of two integers that are > 1
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-- It makes use of the mathematical expression N = A^B
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-- taking Log(N) = Log (A^B) equals to B = Log (N) / Log (A)
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-- where the solutions are when B is an integer > 1
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function Is_Power (N : Integer) return Boolean is
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function Is_Almost_Equal (A : Long_Float;
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B : Long_Float) return Boolean is
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Epsilon : constant := 0.000_000_000_000_001;
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begin
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if abs (A - B) < Epsilon then
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return True;
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else
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return False;
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end if;
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end Is_Almost_Equal;
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A : Integer := 2;
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B : Long_Float;
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Log_Of_N : constant Long_Float := Log (Long_Float (N), 2.0);
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begin
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if N = 1 then
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return True;
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end if;
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while True loop
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B := Log_Of_N / Log (Long_Float (A), 2.0);
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if Is_Almost_Equal (B, Long_Float (Integer (B)))
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and then Integer (B) > 1
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then
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return True;
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end if;
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exit when A * A > N;
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A := @ + 1;
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end loop;
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return False;
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end Is_Power;
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-- An Achilles number is a powerful number that can't be expressed
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-- as a power
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function Is_Achilles (N : Integer) return Boolean is
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begin
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if Is_Powerful (N) then
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if Is_Power (N) = False then
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return True;
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end if;
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end if;
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return False;
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end Is_Achilles;
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-- Calculates the Euler totient of a number
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function Totient (N : Integer) return Integer is
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Tot : Integer := N;
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I : Integer;
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N2 : Integer := N;
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begin
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I := 2;
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while I * I <= N2 loop
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if N2 mod I = 0 then
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while N2 mod I = 0 loop
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N2 := N2 / I;
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end loop;
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Tot := Tot - Tot / I;
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end if;
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if I = 2 then
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I := 1;
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end if;
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I := I + 2;
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end loop;
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if N2 > 1 then
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Tot := Tot - Tot / N2;
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end if;
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return Tot;
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end Totient;
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-- A Strong Achilles number is an Achilles number whose Euler Totient
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-- is also an Achilles number
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function Is_Strong_Achilles (N : Integer) return Boolean is
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begin
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if Is_Achilles (N) then
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if Is_Achilles (Totient (N)) then
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return True;
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end if;
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end if;
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return False;
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end Is_Strong_Achilles;
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-- Counts the digits in a number by taking the string from
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-- its 'Image attribute, trimming it and counting the characters
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function Count_Digits (N : Integer) return Natural is
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Integer_Str : constant String := Trim (N'Image, Both);
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begin
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return Integer_Str'Length;
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end Count_Digits;
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begin
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-- Find the first 50 Achilles numbers
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declare
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N : Integer := 1;
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Count : Integer := 1;
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begin
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Ada.Text_IO.Put_Line ("First 50 Achilles numbers:");
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while Count <= 50 loop
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if Is_Achilles (N) then
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Count := @ + 1;
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Ada.Text_IO.Put (N'Image & " ");
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end if;
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N := @ + 1;
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end loop;
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Ada.Text_IO.New_Line;
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end;
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-- Find the first 20 Strong Achilles numbers
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declare
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N : Integer := 1;
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Count : Integer := 1;
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begin
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Ada.Text_IO.Put_Line ("First 20 Strong Achilles numbers:");
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while Count <= 20 loop
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if Is_Strong_Achilles (N) then
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Count := @ + 1;
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Ada.Text_IO.Put (N'Image & " ");
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end if;
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N := @ + 1;
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end loop;
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Ada.Text_IO.New_Line;
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end;
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-- Count numbers with digits
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declare
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Counts : array (2 .. 6) of Natural := [others => 0];
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N : Integer := 1;
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begin
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Ada.Text_IO.Put_Line ("Number of Achilles numbers with:");
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while Count_Digits (N) <= Counts'Last loop
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-- Ada.Text_IO.Put_Line ("Testing: " & N'Image);
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if Is_Achilles (N) then
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Counts (Count_Digits (N)) := @ + 1;
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end if;
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N := @ + 1;
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end loop;
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for I in Counts'Range loop
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Ada.Text_IO.Put_Line (I'Image & " digits: " & Counts (I)'Image);
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end loop;
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end;
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end Achilles_Numbers;
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@ -1,23 +1,24 @@
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func gcd n d .
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fastfunc gcd n d .
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if d = 0 : return n
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return gcd d (n mod d)
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.
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func totient n .
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for m = 1 to n
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fastfunc totient n .
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m = 1
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while m <= n
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if gcd m n = 1 : tot += 1
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m += 1
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.
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return tot
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.
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func isPowerful m .
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fastfunc isPowerful m .
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n = m
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f = 2
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l = sqrt m
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if m <= 1 : return 0
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while 1 = 1
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q = n div f
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if n mod f = 0
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if m mod (f * f) <> 0 : return 0
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n = q
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n = n div f
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if f > n : return 1
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else
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f += 1
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@ -28,7 +29,7 @@ func isPowerful m .
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.
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.
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.
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func isAchilles n .
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fastfunc isAchilles n .
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if isPowerful n = 0 : return 0
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m = 2
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a = m * m
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@ -46,29 +47,27 @@ func isAchilles n .
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.
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print "First 50 Achilles numbers:"
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n = 1
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repeat
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while cnt < 50
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if isAchilles n = 1
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write n & " "
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num += 1
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cnt += 1
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if cnt mod 10 = 0 : print ""
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.
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n += 1
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until num >= 50
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.
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print ""
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print ""
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print "First 20 strong Achilles numbers:"
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num = 0
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cnt = 0
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n = 1
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repeat
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while cnt < 20
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if isAchilles n = 1 and isAchilles totient n = 1
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write n & " "
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num += 1
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cnt += 1
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if cnt mod 10 = 0 : print ""
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.
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n += 1
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until num >= 20
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.
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print ""
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print ""
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print "Number of Achilles numbers with 2 to 5 digits:"
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a = 10
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b = 100
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@ -1,62 +1,67 @@
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(phixonline)-->
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<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
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<span style="color: #7060A8;">requires</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"1.0.2"</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- [join_by(fmt)]</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
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<span style="color: #008080;">constant</span> <span style="color: #000000;">maxDigits</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()=</span><span style="color: #004600;">JS</span><span style="color: #0000FF;">?</span><span style="color: #000000;">10</span><span style="color: #0000FF;">:</span><span style="color: #000000;">12</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">integer</span> <span style="color: #000000;">pps</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">new_dict</span><span style="color: #0000FF;">()</span>
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with javascript_semantics
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requires("1.0.2") -- [join_by(fmt)]
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atom t0 = time()
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constant maxDigits = iff(platform()=JS?10:12)
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integer pps = new_dict()
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<span style="color: #008080;">procedure</span> <span style="color: #000000;">getPerfectPowers</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">maxExp</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">hi</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">maxExp</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">integer</span> <span style="color: #000000;">imax</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">hi</span><span style="color: #0000FF;">))</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">imax</span> <span style="color: #008080;">do</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">i</span>
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<span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span>
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<span style="color: #000000;">p</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">i</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">>=</span><span style="color: #000000;">hi</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #7060A8;">setd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #004600;">true</span><span style="color: #0000FF;">,</span><span style="color: #000000;">pps</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
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procedure getPerfectPowers(integer maxExp)
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atom hi = power(10, maxExp), t1 = time()+1
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integer imax = floor(sqrt(hi))
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for i=2 to imax do
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atom p = i
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while true do
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p *= i
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if p>=hi then exit end if
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setd(p,true,pps)
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end while
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if time()>t1 then
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progress("getting perfect powers, %d/%d\r",{i,imax})
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t1 = time()+1
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end if
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end for
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progress("")
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end procedure
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<span style="color: #008080;">function</span> <span style="color: #000000;">get_achilles</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">minExp</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">maxExp</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">lo10</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">minExp</span><span style="color: #0000FF;">),</span>
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<span style="color: #000000;">hi10</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">maxExp</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">integer</span> <span style="color: #000000;">bmax</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">hi10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">/</span><span style="color: #000000;">3</span><span style="color: #0000FF;">)),</span>
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<span style="color: #000000;">amax</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">hi10</span><span style="color: #0000FF;">))</span>
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">achilles</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">bmax</span> <span style="color: #008080;">do</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">b3</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">b</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">b</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">b</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">amax</span> <span style="color: #008080;">do</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">b3</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">a</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">a</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">>=</span><span style="color: #000000;">hi10</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">>=</span><span style="color: #000000;">lo10</span> <span style="color: #008080;">then</span>
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<span style="color: #004080;">integer</span> <span style="color: #000000;">node</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">getd_index</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">pps</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">node</span><span style="color: #0000FF;">=</span><span style="color: #004600;">NULL</span> <span style="color: #008080;">then</span>
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<span style="color: #000000;">achilles</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">p</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #000000;">achilles</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">unique</span><span style="color: #0000FF;">(</span><span style="color: #000000;">achilles</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">return</span> <span style="color: #000000;">achilles</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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function get_achilles(integer minExp, maxExp)
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atom lo10 = power(10,minExp),
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hi10 = power(10,maxExp)
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integer bmax = floor(power(hi10,1/3)),
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amax = floor(sqrt(hi10))
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sequence achilles = {}
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for b=2 to bmax do
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atom b3 = b * b * b
|
||||
for a=2 to amax do
|
||||
atom p = b3 * a * a
|
||||
if p>=hi10 then exit end if
|
||||
if p>=lo10 then
|
||||
integer node = getd_index(p,pps)
|
||||
if node=NULL then
|
||||
achilles &= p
|
||||
end if
|
||||
end if
|
||||
end for
|
||||
end for
|
||||
achilles = unique(achilles)
|
||||
return achilles
|
||||
end function
|
||||
|
||||
<span style="color: #000000;">getPerfectPowers</span><span style="color: #0000FF;">(</span><span style="color: #000000;">maxDigits</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">achilles</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">get_achilles</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">)</span>
|
||||
getPerfectPowers(maxDigits)
|
||||
|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">strong_achilles</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">totient</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_eq</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #004600;">true</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">gcd</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">),</span><span style="color: #000000;">n</span><span style="color: #0000FF;">}),</span><span style="color: #000000;">1</span><span style="color: #0000FF;">))</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">totient</span><span style="color: #0000FF;">,</span><span style="color: #000000;">achilles</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
sequence achilles = get_achilles(1,5),
|
||||
a = join_by(achilles[1..50],1,10," ",fmt:="%4d")
|
||||
printf(1,"First 50 Achilles numbers:\n%s\n",{a})
|
||||
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">join_by</span><span style="color: #0000FF;">(</span><span style="color: #000000;">achilles</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">50</span><span style="color: #0000FF;">],</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" "</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">:=</span><span style="color: #008000;">"%4d"</span><span style="color: #0000FF;">),</span>
|
||||
<span style="color: #000000;">sa</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">filter</span><span style="color: #0000FF;">(</span><span style="color: #000000;">achilles</span><span style="color: #0000FF;">,</span><span style="color: #000000;">strong_achilles</span><span style="color: #0000FF;">)[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">30</span><span style="color: #0000FF;">],</span>
|
||||
<span style="color: #000000;">ssa</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">join_by</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sa</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" "</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">:=</span><span style="color: #008000;">"%5d"</span><span style="color: #0000FF;">)</span>
|
||||
function strong_achilles(integer n)
|
||||
integer totient = sum(sq_eq(apply(true,gcd,{tagset(n),n}),1))
|
||||
return find(totient,achilles)
|
||||
end function
|
||||
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"First 50 Achilles numbers:\n%s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">a</span><span style="color: #0000FF;">})</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"First 30 strong Achilles numbers:\n%s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">ssa</span><span style="color: #0000FF;">})</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">maxDigits</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Achilles numbers with %d digits:%d\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">d</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">get_achilles</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d</span><span style="color: #0000FF;">))})</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #0000FF;">?</span><span style="color: #7060A8;">elapsed</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">)</span>
|
||||
<!--
|
||||
progress("filtering strong achilles...")
|
||||
sequence sa = filter(achilles,strong_achilles)[1..30],
|
||||
ssa = join_by(sa,1,10," ",fmt:="%5d")
|
||||
progress("")
|
||||
printf(1,"First 30 strong Achilles numbers:\n%s\n",{ssa})
|
||||
for d=2 to maxDigits do
|
||||
printf(1,"Achilles numbers with %d digits:%d\n",{d,length(get_achilles(d-1,d))})
|
||||
end for
|
||||
?elapsed(time()-t0)
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue