Penholodigital squares: Difference between revisions

Line 48:

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

;* [[First_perfect_square_in_base_n_with_n_unique_digits|Related task: First perfect square in base n with n unique digits]]

=={{header|AppleScript}}==

<syntaxhighlight lang="applescript">on penholodigitalSquares(base)

set digits to "123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"

set output to {}

set minFromDigits to 1

repeat with d from 2 to (base - 1)

set minFromDigits to minFromDigits * base + d

end repeat

set maxFromDigits to base - 1

repeat with d from (base - 2) to 1 by -1

set maxFromDigits to maxFromDigits * base + d

end repeat

repeat with sqrt from (round (minFromDigits ^ 0.5) rounding up) to (maxFromDigits ^ 0.5 div 1)

set n to sqrt * sqrt

set usedDigitValues to {0}

set OKSoFar to true

repeat (base - 2) times -- until (n < base)

set d to n mod base

if (d is in usedDigitValues) then

set OKSoFar to false

exit repeat

end if

set usedDigitValues's end to d

set n to n div base

end repeat

if ((OKSoFar) and (n is not in usedDigitValues)) then ¬

set end of output to {intToBase(sqrt, base), intToBase(sqrt * sqrt, base)}

end repeat

return output

end penholodigitalSquares

on intToBase(int, base)

if ((int < 0) or (int mod 1 > 0) or (base < 2) or (base > 36)) then return missing value

set digits to "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"

set output to digits's character (int mod base + 1)

repeat until (int < base)

set int to int div base

set output to digits's character (int mod base + 1) & output

end repeat

return output

end intToBase

on join(lst, delim)

set astid to AppleScript's text item delimiters

set AppleScript's text item delimiters to delim

set txt to lst as text

set AppleScript's text item delimiters to astid

return txt

end join

on task()

set output to {}

repeat with base from 9 to 14

set results to penholodigitalSquares(base)

set resultCount to (count results)

if (resultCount > 1) then

set output's end to linefeed & "There are " & resultCount & ¬

(" penholodigital squares in base " & base & ":")

if (base < 13) then

repeat with i from 1 to resultCount by 3

set row to {}

set k to i + 2

if (k > resultCount) then set k to resultCount

repeat with j from i to k

set end of row to join(results's item j, " ^ 2 = ")

end repeat

set output's end to join(row, " ")

end repeat

else

set output's end to "First: " & join(results's beginning, " ^ 2 = ") & ¬

(" Last: " & join(results's end, " ^ 2 = "))

end if

else if (resultCount = 1) then

set output's end to linefeed & "There is 1 penholodigital square in base " & ¬

base & ":"

set output's end to join(results's beginning, " ^ 2 = ")

else

set output's end to linefeed & "There are no penholodigital squares in base " & base

end if

end repeat

return join(output, linefeed)

end task

task()</syntaxhighlight>

<syntaxhighlight lang="applescript">"

There are 10 penholodigital squares in base 9:

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

4761 ^ 2 = 25487631 6561 ^ 2 = 47865231 6574 ^ 2 = 48162537

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

8554 ^ 2 = 82314657

There are 30 penholodigital squares in base 10:

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

14676 ^ 2 = 215384976 15681 ^ 2 = 245893761 15963 ^ 2 = 254817369

18072 ^ 2 = 326597184 19023 ^ 2 = 361874529 19377 ^ 2 = 375468129

19569 ^ 2 = 382945761 19629 ^ 2 = 385297641 20316 ^ 2 = 412739856

22887 ^ 2 = 523814769 23019 ^ 2 = 529874361 23178 ^ 2 = 537219684

23439 ^ 2 = 549386721 24237 ^ 2 = 587432169 24276 ^ 2 = 589324176

24441 ^ 2 = 597362481 24807 ^ 2 = 615387249 25059 ^ 2 = 627953481

25572 ^ 2 = 653927184 25941 ^ 2 = 672935481 26409 ^ 2 = 697435281

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

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

There are 20 penholodigital squares in base 11:

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

47149 ^ 2 = 1A67395824 47257 ^ 2 = 1A76392485 52071 ^ 2 = 249A758631

54457 ^ 2 = 2719634A85 55979 ^ 2 = 286A795314 59597 ^ 2 = 314672A895

632A4 ^ 2 = 3671A89245 64069 ^ 2 = 376198A254 68335 ^ 2 = 41697528A3

71485 ^ 2 = 46928A7153 81196 ^ 2 = 5A79286413 83608 ^ 2 = 632A741859

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

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

There are 23 penholodigital squares in base 12:

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

16906B ^ 2 = 25386749BA1 173434 ^ 2 = 26B859A3714 178278 ^ 2 = 2835BA17694

1A1993 ^ 2 = 34A8125B769 1A3595 ^ 2 = 354A279B681 1B0451 ^ 2 = 3824B7569A1

1B7545 ^ 2 = 3A5B2487961 2084A9 ^ 2 = 42A1583B769 235273 ^ 2 = 5287BA13469

2528B5 ^ 2 = 5B23A879641 25B564 ^ 2 = 62937B5A814 262174 ^ 2 = 63A8527B194

285A44 ^ 2 = 73B615A8294 29A977 ^ 2 = 7B9284A5361 2A7617 ^ 2 = 83AB5479261

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

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

There are no penholodigital squares in base 13

There are 160 penholodigital squares in base 14:

First: 1129535 ^ 2 = 126A84D79C53B Last: 3A03226 ^ 2 = DB3962A7541C8"</syntaxhighlight>

=={{header|Delphi}}==