Data commit

Task/Magic-constant/Free-Pascal/magic-constant.pas

@@ -0,0 +1,40 @@
+program MagicConst;
+{$IFDEF FPC}{$MODE DELPHI}{$OPTIMIZATION ON,ALL}{$ENDIF}
+{$IFDEF WINDOWS}{$APPTYPE CONSOLE}{$ENDIF}
+
+function MagicSum(n :Uint32):Uint64; inline;
+var
+  k : Uint64;
+begin
+  k := n*Uint64(n);
+  result := (k*k+k) DIV 2;
+end;
+
+function MagSumPerRow(n:Uint32):Uint32;
+begin
+//result := MagicSum(n) DIV n;
+  //(n^3 + n) /2
+  result := ((Uint64(n)*n+1)*n) DIV 2;
+end;
+var
+  s : String[31];
+  i : Uint32;
+  lmt,rowcnt : extended;
+Begin
+  writeln('First Magic constants 3..20');
+  For i := 3 to 20 do
+     write(MagSumPerRow(i),' ');
+  writeln;
+  writeln('1000.th ',MagSumPerRow(1002));
+
+  writeln('First Magic constants > 10^xx');
+  //lmt = (rowcnt^3 + rowcnt) /2 -> rowcnt > (lmt*2 )^(1/3)
+  lmt := 2.0 * 10.0;
+  For i :=  1 to 50 do
+  begin
+    rowcnt := Int(exp(ln(lmt)/3))+1.0;//+1 suffices
+    str(trunc(rowcnt),s);
+    writeln('10^',i:2,#9,s:18);
+    f := 10.0*lmt;
+  end;
+end.