Magic constant: Difference between revisions
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10^49 27144176165949066
10^50 58480354764257322</pre>
=={{header|Pascal}}==
==={{header|Free Pascal}}===
<syntaxhighlight lang="pascal">
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.</syntaxhighlight>
{{out}}
<pre>
First Magic constants 3..20
15 34 65 111 175 260 369 505 671 870 1105 1379 1695 2056 2465 2925 3439 4010
1000.th 503006505
First Magic constants > 1=0^xx
10^ 1 3
10^ 2 6
10^ 3 13
10^ 4 28
10^ 5 59
10^ 6 126
10^ 7 272
10^ 8 585
10^ 9 1260
10^10 2715
10^11 5849
10^12 12600
10^13 27145
10^14 58481
10^15 125993
10^16 271442
10^17 584804
10^18 1259922
10^19 2714418
10^20 5848036
... same as Mathematica
10^46 2714417616594907
10^47 5848035476425733
10^48 12599210498948732
10^49 27144176165949066
10^50 58480354764257322</pre>
=={{header|Perl}}==
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