Penholodigital squares: Difference between revisions

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=={{header|Pascal}}==

==={{header|Free Pascal}}===

nearly copy and paste of pandigital square numbers.~~base 17 none found.Base 18 starts late, base 19 no start found within 20 min.~~

nearly copy and paste of pandigital square numbers.<BR>

Calc GCD of deltas between the roots.Mostly not 1.<BR>

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base 17 none found.Base 18 starts late, base 19 no start found within 20 min.

program penholodigital;

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<syntaxhighlight lang="pascal">program penholodigital;

//Find the smallest number n to base b, so that n*n includes all

//digits of base b without 0

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var

sl : array of string;

s2Delta : array of Uint32;

Num,

sqr2B,

deltaNum : tNumtoBase;

function gcd(A, B: Uint32): Uint32;

var

Rest: Uint32;

begin

while B <> 0 do

begin

Rest := A mod B;

A := B;

B := Rest;

end;

Result := A;

end;

procedure Conv2num(var num:tNumtoBase;n:Uint64;base:NativeUint);

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Begin

setlength(sl,740);

setlength(s2Delta,740);

//number containing 1,2..,base-1

n := 0;

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Begin

IncNumBig(num,i);

sl[penHoloCnt] := ~~OutNum(Num)+'^2 = '+OutNum(sqr2B)~~;

s2delta[penHoloCnt] := i;

sl[penHoloCnt] := Format('%s^2 = %s',[OutNum(Num),OutNum(sqr2B)]);

inc(penHoloCnt);

i := 0;

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inc(i);

until sqr2B.ntb_cnt >= base;

Writeln('There are a total of ',penHoloCnt,' penholodigital squares in base: ',base:2);

if (penHoloCnt > 0) AND (base < 14) then

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write(',',sl[j]);

writeln;

end;

end

else

if penHoloCnt > 0 then

begin

writeln(sl[0],',',sl[penHoloCnt-1]);

end;

j := 1;

IF penHoloCnt> 4 then

Begin

//omit first delta s2delta[0], caused by estimaing first value

j := gcd(s2delta[1],s2delta[2]);

For i := penHoloCnt-1 downto 3 do

begin

j := gcd(s2delta[i],j);

IF j = 1 then

BREAK;

end;

writeln('GGT of delta :',j);

end;

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There are a total of 1 penholodigital squares in base: 2

1^2 = 1

GCD of delta :1

There are a total of 0 penholodigital squares in base: 3

GCD of delta :1

There are a total of 0 penholodigital squares in base: 4

GCD of delta :1

There are a total of 0 penholodigital squares in base: 5

GCD of delta :1

There are a total of 2 penholodigital squares in base: 6

122^2 = 15324,221^2 = 53241

GCD of delta :1

There are a total of 1 penholodigital squares in base: 7

645^2 = 623514

GCD of delta :1

There are a total of 1 penholodigital squares in base: 8

2453^2 = 6532471

GCD of delta :1

There are a total of 10 penholodigital squares in base: 9

3825^2 = 16328547,3847^2 = 16523874,4617^2 = 23875614

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6844^2 = 53184267,7285^2 = 58624317,7821^2 = 68573241

8554^2 = 82314657

GCD of delta :4

There are a total of 30 penholodigital squares in base: 10

11826^2 = 139854276,12363^2 = 152843769,12543^2 = 157326849

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26733^2 = 714653289,27129^2 = 735982641,27273^2 = 743816529

29034^2 = 842973156,29106^2 = 847159236,30384^2 = 923187456

GCD of delta :3

There are a total of 20 penholodigital squares in base: 11

42045^2 = 165742A893,43152^2 = 173A652894,44926^2 = 18792A6453

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86074^2 = 6713498A25,89468^2 = 7148563A29,91429^2 = 76315982A4

93319^2 = 795186A234,A3A39^2 = 983251A764

GCD of delta :10

There are a total of 23 penholodigital squares in base: 12

117789^2 = 135B7482A69,16357B^2 = 23A5B976481,16762B^2 = 24AB5379861

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2B0144^2 = 8617B35A294,307381^2 = 93825A67B41,310828^2 = 96528AB7314

319488^2 = 9AB65823714,319A37^2 = 9B2573468A1

GCD of delta :11

There are a total of 0 penholodigital squares in base: 13

GCD of delta :1

There are a total of 160 penholodigital squares in base: 14

1129535^2 = 126A84D79C53B,3A03226^2 = DB3962A7541C8

GCD of delta :13

There are a total of 419 penholodigital squares in base: 15

4240C58^2 = 12378DA5B6EC94,EE25E4A^2 = ED4C93285671BA

GCD of delta :14

There are a total of 740 penholodigital squares in base: 16

11156EB6^2 = 123DA7F85BCE964,3FD8F786^2 = FEC81B69573DA24

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Total runtime in s 50.~~755~~

GCD of delta :15

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Total runtime in s 50.873

@home:

@home:Total runtime in s 18.130

There are a total of 0 penholodigital squares in base: 17 ( 1min 47 ~~for this~~ )

There are a total of 0 penholodigital squares in base: 17 ( 1min 47 )

Starting base 18 takes a lot of time

base 18 delta

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112237HG2^2 = 1258FDG67B9CHE3A4 17,051

1122775FB^2 = 1259637EGF84AHBCD 416,007

....stopped

....stopped // GCD of delta 17 ? )

base 19 no startvalue after 20 min..

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