Data update

Task/Magic-constant/ANSI-BASIC/magic-constant.basic

@@ -0,0 +1,25 @@
+100 REM Magic constant
+110 DECLARE EXTERNAL FUNCTION A
+120 DECLARE EXTERNAL FUNCTION InvA
+130 PRINT "The first 20 magic constants are";
+140 FOR N = 1 TO 20
+150    PRINT A(N);
+160 NEXT N
+170 PRINT
+180 PRINT "The 1,000th magic constant is"; A(1000)
+190 LET E = 1
+200 FOR N = 1 TO 20
+210    LET E = E * 10
+220    PRINT "10^";
+230    PRINT USING "##: #########": N, InvA(E)
+240 NEXT N
+250 END
+260 REM Returns the magic constant of a magic square of order N + 2
+270 EXTERNAL FUNCTION A(N)
+280 LET N2 = N + 2
+290 LET A = IP((N2 * ((N2 * N2) + 1)) / 2)
+300 END FUNCTION
+310 REM Returns the order of the magic square whose magic constant is at least X
+320 EXTERNAL FUNCTION InvA(X)
+330 LET InvA = IP((2 * X) ^ (1 / 3)) + 1
+340 END FUNCTION

Task/Magic-constant/C/magic-constant.c

@@ -0,0 +1,32 @@
+/* Magic constant */
+#include<stdio.h>
+#include<math.h>
+
+/* returns the magic constant of a magic square of order n + 2 */
+long a(int n)
+{
+  long n2 = n + 2;
+  return (n2 * ((n2 * n2) + 1)) / 2;
+}
+
+/* returns the order of the magic square whose magic constant is at least x */
+long inv_a(double x)
+{
+  return (long)pow((2. * x), 1. / 3.) + 1;
+}
+
+int main()
+{
+  int n;
+  double e = 1.; /* final values can be greater than MAX_LONG */
+  printf("The first 20 magic constants are ");
+  for (n = 1; n <= 20; n++)
+    printf("%d ", a(n));
+  printf("\n");
+  printf("The 1,000th magic constant is %d\n", a(1000));
+  for (n = 1; n <= 20; n++)
+  {
+    e *= 10;
+    printf("10^%2d: %9d\n", n, inv_a(e));
+  }
+}

Task/Magic-constant/GW-BASIC/magic-constant.basic

@@ -0,0 +1,24 @@
+100 REM Magic constant
+110 PRINT "First 20 magic constants:";
+120 FOR N = 3 TO 20 + 3 - 1
+130  PRINT (N * N * N + N) / 2;
+140 NEXT N
+150 PRINT
+160 PRINT "1000th magic constant: ";
+170 N# = 1000! + 3 - 1
+180 MC1000# = INT((N# * N# * N# + N#) / 2)
+190 PRINT USING "#########"; MC1000#
+200 PRINT "Smallest order magic square with a constant greater than:"
+210 THRESH# = 10
+220 M# = 3
+230 FOR X = 1 TO 20
+240   MC# = (M# * M# * M# + M#) / 2
+250   M# = M# + 1
+260  IF MC# <= THRESH# THEN 240
+270  PRINT "10^";
+280  PRINT USING "##:"; X;
+290  PRINT USING "########"; M# - 1;
+300  THRESH# = THRESH# * 10
+310  IF X MOD 5 = O THEN PRINT ELSE PRINT "| ";
+320 NEXT X
+330 END

Task/Magic-constant/Gambas/magic-constant.gambas

@@ -0,0 +1,35 @@
+Function a(n As Integer) As Long
+
+  n += 2
+  Return n * (n ^ 2 + 1) / 2
+
+End Function
+
+Function inv_a(x As Float) As Long
+
+  Dim k As Long = 0
+
+  While k * (k ^ 2 + 1) / 2 + 2 < x
+    k += 1
+  Wend
+  Return k
+
+End Function
+
+Public Sub Main()
+
+  Dim n As Long
+
+  Print "The first 20 magic constants are: "
+
+  For n = 1 To 20
+    Print a(n); " ";
+  Next
+  Print
+  Print "The 1,000th magic constant is "; a(1000)
+
+  For e As Integer = 1 To 20
+    Print "10^"; Format(e, "##"); ": "; Format(inv_a(10 ^ e), "#########")
+  Next
+
+End Sub

Task/Magic-constant/Modula-2/magic-constant.mod2

@@ -0,0 +1,46 @@
+MODULE MagicConstant;
+
+FROM STextIO IMPORT WriteString, WriteLn;
+FROM SWholeIO IMPORT WriteInt;
+FROM RealMath IMPORT exp, ln;
+
+VAR
+  N: CARDINAL;
+  E: REAL;
+
+(* Returns the magic constant of a magic square of order N + 2 *)
+PROCEDURE A(N: CARDINAL): CARDINAL;
+VAR
+  N2: CARDINAL;
+BEGIN
+  N2 := N + 2;
+  RETURN (N2 * ((N2 * N2) + 1)) DIV 2
+END A;
+
+(* Returns the order of the magic square whose magic constant is at least X *)
+PROCEDURE InvA(X: REAL): CARDINAL;
+BEGIN
+  RETURN VAL(INTEGER, exp(ln((2. * X)) / 3.) + 1.)
+  (* Use of power(2. * X, 1. / 3.) + 1. does not give enough precision due to rounded exponent *)
+END InvA;
+
+BEGIN
+  WriteString("The first 20 magic constants are ");
+  FOR N := 1 TO 20 DO
+    WriteInt(A(N), 1);
+    WriteString(" ")
+  END;
+  WriteLn;
+  WriteString("The 1,000th magic constant is ");
+  WriteInt(A(1000), 1);
+  WriteLn;
+  E := 1.;
+  FOR N := 1 TO 20 DO (* The results are equal to these from Mathematica for N <= 23 *)
+    E := E * 10.;
+    WriteString("10^");
+    WriteInt(N, 2);
+    WriteString(": ");
+    WriteInt(InvA(E), 9);
+    WriteLn
+  END
+END MagicConstant.

Task/Magic-constant/PHP/magic-constant.php

@@ -0,0 +1,27 @@
+<?php
+// Magic constant
+
+// Returns the magic constant of a magic square of order $n + 2
+function a($n) {
+  $n2 = $n + 2;
+  return floor(($n2 * (($n2 * $n2) + 1)) / 2);
+}
+
+// Returns the order of the magic square whose magic constant is at least $x
+function inv_a($x) {
+  return floor(pow(2 * $x, 1 / 3) + 1);
+}
+
+echo("The first 20 magic constants are ");
+for ($n = 1; $n <= 20; $n++)
+  echo(a($n)." ");
+echo(PHP_EOL);
+echo("The 1,000th magic constant is ".a(1000).PHP_EOL);
+$e = 1;
+for ($n = 1; $n <= 20; $n++) {
+  $e *= 10;
+  echo("10^".str_pad($n, 2, ' ', STR_PAD_LEFT));
+  echo(": ".str_pad(inv_a($e), 9, ' ', STR_PAD_LEFT));
+  echo(PHP_EOL);
+}
+?>

Task/Magic-constant/REXX/magic-constant.rexx

@@ -0,0 +1,62 @@
+-- 8 May 2025
+include Settings
+
+say 'MAGIC CONSTANT'
+say version
+say
+numeric digits 23
+call Getmagics 6e8
+call Task1
+call Task2
+call Task3
+exit
+
+Getmagics:
+call Time('r')
+arg xx
+say 'Get magic constants up to' xx
+say Magics(xx) 'collected'
+say Format(Time('e'),,3) 'seconds'
+say
+return
+
+Task1:
+call Time('r')
+say 'The first 25 magic constants are'
+do i = 3 to 28
+   call Charout ,magi.i' '
+end
+say
+say Format(Time('e'),,3) 'seconds'
+say
+return
+
+Task2:
+call Time('r')
+say 'The 1000th magic constant is'
+say magi.1002
+say Format(Time('e'),,3) 'seconds'
+say
+return
+
+Task3:
+call Time('r')
+say 'Smallest magic square with constant > 10^n is'
+say Left('n',5) Right('order',8)
+say '--------------'
+e = 1
+do i = 3 to 6e7
+   if Magic(i) > 1'E'e then do
+      say Left('10^'e,5) Right(i,8)
+      e = e+1
+   end
+end
+say '--------------'
+say Format(Time('e'),,3) 'seconds'
+say
+return
+
+include Functions
+include Sequences
+include Numbers
+include Abend

Task/Magic-constant/Tiny-BASIC/magic-constant.basic

@@ -0,0 +1,21 @@
+10 REM MAGIC CONSTANT
+20 PRINT "FIRST 20 MAGIC CONSTANTS:"
+30 LET N=3
+40 IF N>20+3-1 GOTO 80
+50 PRINT (N*N*N+N)/2,
+60 LET N=N+1
+70 GOTO 40
+80 PRINT
+90 PRINT "SMALLEST ORDER MAGIC SQUARE WITH A CONSTANT GREATER THAN:"
+100 LET T=10
+110 LET M=3
+120 LET X=1
+130 LET L=(M*M*M+M)/2
+140 LET M=M+1
+150 IF L<=T GOTO 130
+160 PRINT "10^";X;":",M-1
+170 LET X=X+1
+180 IF X>4 GOTO 210
+190 LET T=T*10
+200 GOTO 130
+210 END