Increasing gaps between consecutive Niven numbers: Difference between revisions

=={{header|Delphi}}==

{{works with|Delphi|6.0}}

{{libheader|Windows,SysUtils,StdCtrls}}

Because the code requires almost two minutes to run, it has optional callback that supplies information that can be used to power a progress bar.

<syntaxhighlight lang="Delphi">

function SumDigits(N: integer): integer;

{Sum the integers in a number}

var T: integer;

begin

Result:=0;

repeat

begin

T:=N mod 10;

N:=N div 10;

Result:=Result+T;

end

until N<1;

end;

function IsNiven(N: integer): boolean;

{Test if N is evenly divisible by sum}

{i.e. is it a Niven Number}

var Sum: integer;

begin

Sum:=SumDigits(N);

Result:=(N mod Sum)=0;

end;

function GetNextNiven(Start: integer): integer;

{Get the next Niven number after Start}

begin

repeat Inc(Start)

until IsNiven(Start);

Result:=Start;

end;

procedure ShowNivenGaps(Memo: TMemo; Prog: TProgress);

{Show when gaps between sucessive Niven Numbers changes}

var I: integer;

var N1,N2,Gap: integer;

var Cnt: integer;

const Limit = 65000000;

begin

Memo.Lines.Add(' Gap Gap Niven Niven Next');

Memo.Lines.Add('Index Value Index Number Niven Number');

Memo.Lines.Add('----- ----- -------- --------- ------------');

Gap:=0; Cnt:=0;

N1:=GetNextNiven(0);

for I:=1 to Limit do

begin

{Get next Niven and test if Gap has changed}

N2:=GetNextNiven(N1);

if (N2-N1)>Gap then

begin

Gap:=N2-N1;

Inc(Cnt);

Memo.Lines.Add(Format('%5d%6d%15.0n%15.0n%15.0n',[Cnt,Gap,I+0.0,N1+0.0,N2+0.0]));

end;

N1:=N2;

if Assigned(Prog) and ((I mod 100000)=0) then Prog(MulDiv(100,I,Limit));

end;

end;

</syntaxhighlight>

{{out}}

<pre>

Gap Gap Niven Niven Next

Index Value Index Number Niven Number

----- ----- -------- --------- ------------

1 1 1 1 2

2 2 10 10 12

3 6 11 12 18

4 7 26 63 70

5 8 28 72 80

6 10 32 90 100

7 12 83 288 300

8 14 102 378 392

9 18 143 558 576

10 23 561 2,889 2,912

11 32 716 3,784 3,816

12 36 1,118 6,480 6,516

13 44 2,948 19,872 19,916

14 45 4,194 28,971 29,016

15 54 5,439 38,772 38,826

16 60 33,494 297,864 297,924

17 66 51,544 478,764 478,830

18 72 61,588 589,860 589,932

19 88 94,748 989,867 989,955

20 90 265,336 2,879,865 2,879,955

21 99 800,054 9,898,956 9,899,055

22 108 3,750,017 49,989,744 49,989,852

23 126 6,292,149 88,996,914 88,997,040

24 135 44,194,186 689,988,915 689,989,050

25 144 55,065,654 879,987,906 879,988,050

26 150 61,074,615 989,888,823 989,888,973

</pre>