Penholodigital squares: Difference between revisions

;See also

;* [[oeis:A036744|OEIS:A036744 - Penholodigital squares in base 10]]

 

 

=={{header|Go}}==

def convert(base):

def stream:

| if base < 10 then map(tostring) | join("")

elif base <= 36 then map(if . < 10 then 48 + . else . + 87 end) | implode

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

11156eb6² = 123da7f85bce964 3fd8f786² = fec81b69573da24

</pre>

 

=={{header|Pascal}}==

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

<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

{$IFDEF FPC}{$MODE DELPHI}{$Optimization ON,All}{$ENDIF}

uses

sysutils;

type

tNumtoBase = record

ntb_cnt,

end;

var

sl : array of string;

s2Delta : array of Uint32;

Num,

sqr2B,

 

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

end;

end;

 

procedure IncNumBig(var add1:tNumtoBase;n:NativeUInt);

end;

 

var

n,penHoloCnt : Uint64;

Begin

penHoloCnt := 0;

repeat

begin

j := 0;

end

else

begin

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

end;

end;

 

begin

T0 := now;

Test(base);

writeln('Total runtime in s ',(now-T0)*86400:10:3);

{{out|@TIO.RUN}}

<pre style="height:40ex;overflow:scroll;">

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

1^2 = 1

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

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

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

122^2 = 15324,221^2 = 53241

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

645^2 = 623514

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

2453^2 = 6532471

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

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

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

8554^2 = 82314657

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

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

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

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

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

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

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

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

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

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

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

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

 

</pre>

 

=={{header|Raku}}==

 

Although I'm not quite sure why, it appears that a necessary condition for a number to be a penholodigital square is for its square root to be exactly divisible by the highest prime factor of (base - 1).

import "./fmt" for Conv, Fmt

 

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

1129535² = 126A84D79C53B 3A03226² = DB3962A7541C8

</pre>