Data update
This commit is contained in:
Ingy döt Net
parent
5150844a7d
commit
4bb20c9b71
7735 changed files with 38060 additions and 199180 deletions
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@ -2,7 +2,7 @@ brazilian?: function [n][
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if n < 7 -> return false
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if zero? and n 1 -> return true
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loop 2..n-2 'b [
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if 1 = size unique digits.base:b n ->
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if one? unique digits.base:b n ->
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return true
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]
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return false
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@ -11,11 +11,11 @@ brazilian?: function [n][
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printFirstByRule: function [rule,title][
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print ~"First 20 |title|brazilian numbers:"
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i: 7
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found: new []
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found: []
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while [20 > size found][
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if brazilian? i ->
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'found ++ i
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do.import rule
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do rule
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]
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print found
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print ""
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@ -1,292 +0,0 @@
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program brazilianNumbers;
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{$IFDEF FPC}
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{$MODE DELPHI}{$OPTIMIZATION ON,All}
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{$CODEALIGN proc=32,loop=4}
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{$ELSE}
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{$APPTYPE CONSOLE}
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{$ENDIF}
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uses
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SysUtils;
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const
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//Must not be a prime
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PrimeMarker = 0;
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SquareMarker = PrimeMarker + 1;
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//MAX = 110468;// 1E5 brazilian
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//MAX = 1084566;// 1E6 brazilian
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//MAX = 10708453;// 1E7 brazilian
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//MAX = 106091516;// 1E8 brazilian
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MAX = 1053421821;// 1E9 brazilian
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var
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isprime: array of word;
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procedure MarkSmallestFactor;
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//sieve of erathotenes
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//but saving the smallest factor
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var
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i, j, lmt: NativeUint;
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begin
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lmt := High(isPrime);
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fillWord(isPrime[0], lmt + 1, PrimeMarker);
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//mark even numbers
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i := 2;
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j := i * i;
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isPrime[j] := SquareMarker;
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Inc(j, 2);
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while j <= lmt do
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begin
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isPrime[j] := 2;
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Inc(j, 2);
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end;
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//mark 3 but not 2
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i := 3;
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j := i * i;
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isPrime[j] := SquareMarker;
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Inc(j, 6);
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while j <= lmt do
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begin
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isPrime[j] := 3;
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Inc(j, 6);
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end;
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i := 5;
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while i * i <= lmt do
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begin
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if isPrime[i] = 0 then
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begin
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j := lmt div i;
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if not (odd(j)) then
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Dec(j);
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while j > i do
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begin
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if isPrime[j] = 0 then
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isPrime[i * j] := i;
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Dec(j, 2);
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end;
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//mark square prime
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isPrime[i * i] := SquareMarker;
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end;
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Inc(i, 2);
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end;
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end;
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procedure OutFactors(n: NativeUint);
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var
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divisor, Next, rest: NativeUint;
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pot: NativeUint;
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begin
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divisor := 2;
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Next := 3;
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rest := n;
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Write(n: 10, ' = ');
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while (rest <> 1) do
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begin
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if (rest mod divisor = 0) then
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begin
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Write(divisor);
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pot := 0;
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repeat
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rest := rest div divisor;
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Inc(pot)
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until rest mod divisor <> 0;
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if pot > 1 then
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Write('^', pot);
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if rest > 1 then
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Write('*');
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end;
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divisor := Next;
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Next := Next + 2;
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// cut condition: avoid many useless iterations
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if (rest <> 1) and (rest < divisor * divisor) then
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begin
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Write(rest);
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rest := 1;
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end;
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end;
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Write(' ', #9#9#9);
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end;
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procedure OutToBase(number, base: NativeUint);
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var
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BaseDgt: array[0..63] of NativeUint;
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i, rest: NativeINt;
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begin
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OutFactors(number);
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i := 0;
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while number <> 0 do
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begin
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rest := number div base;
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BaseDgt[i] := number - rest * base;
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number := rest;
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Inc(i);
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end;
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while i > 1 do
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begin
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Dec(i);
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Write(BaseDgt[i]);
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end;
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writeln(BaseDgt[0], ' to base ', base);
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end;
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function PrimeBase(number: NativeUint): NativeUint;
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var
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lnN: extended;
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i, exponent, n: NativeUint;
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begin
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// primes are only brazilian if 111...11 to base > 2
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// the count of "1" must be odd , because brazilian primes are odd
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lnN := ln(number);
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exponent := 4;
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//result := exponent.th root of number
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Result := trunc(exp(lnN*0.25));
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while result >2 do
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Begin
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// calc sum(i= 0 to exponent ) base^i;
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n := Result + 1;
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i := 2;
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repeat
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Inc(i);
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n := n*result + 1;
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until i > exponent;
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if n = number then
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EXIT;
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Inc(exponent,2);
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Result := trunc(exp(lnN/exponent));
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end;
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//not brazilian
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Result := 0;
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end;
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function GetPrimeBrazilianBase(number: NativeUint): NativeUint;
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//result is base
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begin
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// prime of 2^n - 1
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if (Number and (number + 1)) = 0 then
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Result := 2
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else
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begin
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Result := trunc(sqrt(number));
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//most of the brazilian primes are of this type base^2+base+1
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IF (sqr(result)+result+1) <> number then
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result := PrimeBase(number);
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end;
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end;
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function GetBrazilianBase(number: NativeUInt): NativeUint; inline;
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begin
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Result := isPrime[number];
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if Result > SquareMarker then
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Result := (number div Result) - 1
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else
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begin
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if Result = SquareMarker then
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begin
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if number = 121 then
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Result := 3
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else
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Result := 0;
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end
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else
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Result := GetPrimeBrazilianBase(number);
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end;
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end;
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procedure First20Brazilian;
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var
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i, n, cnt: NativeUInt;
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begin
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writeln('first 20 brazilian numbers');
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i := 7;
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cnt := 0;
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while cnt < 20 do
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begin
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n := GetBrazilianBase(i);
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if n <> 0 then
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begin
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Inc(cnt);
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OutToBase(i, n);
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end;
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Inc(i);
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end;
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writeln;
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end;
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procedure First33OddBrazilian;
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var
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i, n, cnt: NativeUInt;
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begin
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writeln('first 33 odd brazilian numbers');
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i := 7;
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cnt := 0;
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while cnt < 33 do
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begin
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n := GetBrazilianBase(i);
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if N <> 0 then
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begin
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Inc(cnt);
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OutToBase(i, n);
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end;
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Inc(i, 2);
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end;
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writeln;
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end;
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procedure First20BrazilianPrimes;
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var
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i, n, cnt: NativeUInt;
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begin
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writeln('first 20 brazilian prime numbers');
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i := 7;
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cnt := 0;
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while cnt < 20 do
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begin
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IF isPrime[i] = PrimeMarker then
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Begin
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n := GetBrazilianBase(i);
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if n <> 0 then
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begin
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Inc(cnt);
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OutToBase(i, n);
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end;
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end;
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Inc(i);
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end;
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writeln;
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end;
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var
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T1, T0: TDateTime;
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i, n, cnt, lmt: NativeUInt;
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begin
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lmt := MAX;
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setlength(isPrime, lmt + 1);
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MarkSmallestFactor;
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First20Brazilian;
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First33OddBrazilian;
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First20BrazilianPrimes;
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Write('count brazilian numbers up to ', lmt, ' = ');
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T0 := now;
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i := 7;
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cnt := 0;
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n := 0;
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while (i <= lmt) do
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begin
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Inc(n, Ord(isPrime[i] = PrimeMarker));
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if GetBrazilianBase(i) <> 0 then
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Inc(cnt);
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Inc(i);
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end;
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T1 := now;
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writeln(cnt);
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writeln('Count of primes ', n: 11+13);
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writeln((T1 - T0) * 86400 * 1000: 10: 0, ' ms');
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setlength(isPrime, 0);
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end.
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@ -1,56 +1,54 @@
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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: #008080;">function</span> <span style="color: #000000;">same_digits</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: #000000;">b</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">integer</span> <span style="color: #000000;">f</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">/</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">while</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">></span><span style="color: #000000;">0</span> <span style="color: #008080;">do</span>
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<span style="color: #008080;">if</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)!=</span><span style="color: #000000;">f</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #004600;">false</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">/</span><span style="color: #000000;">b</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;">return</span> <span style="color: #004600;">true</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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with javascript_semantics
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function same_digits(integer n, b)
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integer f = remainder(n,b)
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n = floor(n/b)
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while n>0 do
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if remainder(n,b)!=f then return false end if
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n = floor(n/b)
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end while
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return true
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end function
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<span style="color: #008080;">function</span> <span style="color: #000000;">is_brazilian</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">>=</span><span style="color: #000000;">7</span> <span style="color: #008080;">then</span>
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<span style="color: #008080;">if</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #004600;">true</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</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;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">same_digits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #004600;">true</span> <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;">if</span>
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<span style="color: #008080;">return</span> <span style="color: #004600;">false</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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function is_brazilian(integer n)
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if n>=7 then
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if remainder(n,2)=0 then return true end if
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for b=2 to n-2 do
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if same_digits(n,b) then return true end if
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end for
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end if
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return false
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end function
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<span style="color: #008080;">constant</span> <span style="color: #000000;">kinds</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #008000;">" "</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">" odd "</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">" prime "</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;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">kinds</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
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<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 20%sBrazilian numbers:\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">kinds</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]})</span>
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<span style="color: #004080;">integer</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">4</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: #008080;">if</span> <span style="color: #000000;">is_brazilian</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
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<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;">"%d "</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">c</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">==</span><span style="color: #000000;">20</span> <span style="color: #008080;">then</span>
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<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;">"\n\n"</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">exit</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;">switch</span> <span style="color: #000000;">i</span>
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<span style="color: #008080;">case</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">:</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
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<span style="color: #008080;">case</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">:</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">2</span>
|
||||
<span style="color: #008080;">case</span> <span style="color: #000000;">3</span><span style="color: #0000FF;">:</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">;</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">get_prime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">switch</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
constant kinds = {" ", " odd ", " prime "}
|
||||
for i=1 to length(kinds) do
|
||||
printf(1,"First 20%sBrazilian numbers:\n", {kinds[i]})
|
||||
integer c = 0, n = 7, p = 4
|
||||
while true do
|
||||
if is_brazilian(n) then
|
||||
printf(1,"%d ",n)
|
||||
c += 1
|
||||
if c==20 then
|
||||
printf(1,"\n\n")
|
||||
exit
|
||||
end if
|
||||
end if
|
||||
switch i
|
||||
case 1: n += 1
|
||||
case 2: n += 2
|
||||
case 3: p += 1; n = get_prime(p)
|
||||
end switch
|
||||
end while
|
||||
end for
|
||||
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
|
||||
<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> <span style="color: #000000;">t1</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()+</span><span style="color: #000000;">1</span>
|
||||
<span style="color: #008080;">while</span> <span style="color: #000000;">c</span><span style="color: #0000FF;"><</span><span style="color: #000000;">100000</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()!=</span><span style="color: #004600;">JS</span> <span style="color: #008080;">and</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()></span><span style="color: #000000;">t1</span> <span style="color: #008080;">then</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;">"checking %d [count:%d]...\r"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">})</span>
|
||||
<span style="color: #000000;">t1</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()+</span><span style="color: #000000;">1</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #000000;">c</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">is_brazilian</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: #008080;">end</span> <span style="color: #008080;">while</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;">"The %,dth Brazilian number: %d\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">c</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: #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>
|
||||
<!--
|
||||
integer n = 7, c = 0
|
||||
atom t0 = time(), t1 = time()+1
|
||||
while c<100000 do
|
||||
if platform()!=JS and time()>t1 then
|
||||
printf(1,"checking %d [count:%d]...\r",{n,c})
|
||||
t1 = time()+1
|
||||
end if
|
||||
c += is_brazilian(n)
|
||||
n += 1
|
||||
end while
|
||||
printf(1,"The %,dth Brazilian number: %d\n", {c,n-1})
|
||||
?elapsed(time()-t0)
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue