Penholodigital squares: Difference between revisions

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=={{header|Phix}}==

using string maths (and not particularly fast)

with javascript_semantics

procedure penholodigital(integer base)

sequence penholodigitals = {}

-- search squares of n from eg for base=4 sqrt(123)

-- (and stop when next square has too many digits)

atom n = 0, t1 = time()+1, carry = 0

for d=1 to base-1 do n = n*base+d end for

n = ceil(sqrt(n)) assert(integer(n))

string digits = "123456789ABCDEF"[1..base-1],

square = sprintf("%A",{{base,n*n}})

integer div = prime_factors(base-1,true)[$]

bool ndz = mod(n,div)=0

while true do -- (until we get a carry off the end of square)

if ndz and not find('0',square) and sort(square)=digits then

penholodigitals &= {{{base,n},square}} -- (fmt later)

end if

-- add 2n+1 to get the next square (using string maths)

carry += 2*n+1

n += 1

ndz = mod(n,div)=0

if ndz then

integer d = base-1

while carry and d do

atom ch = square[d]

ch += carry - iff(ch<='9'?'0':'A'-10)

carry = floor(ch/base)

ch = remainder(ch,base)

square[d] = ch + iff(ch<=9?'0':'A'-10)

d -= 1

end while

if carry then exit end if

if time()>t1 then

integer l = length(penholodigitals),

e = {1,0,0,0,2,1,1,10,30,20,23,0,160,419,740}[base-1]

progress("scanning base %d, %s (%d/%d found)\r",{base,square,l,e})

t1 = time()+1

end if

end while

progress("")

integer count = length(penholodigitals)

if base>12 and count>2 then

penholodigitals = extract(penholodigitals,{1,-1})

end if

penholodigitals = apply(true,sprintf,{{"%A**2 = %s"},penholodigitals})

string p = iff(count?":\n"&iff(base>12?sprintf("%s .. %s\n",penholodigitals)

:join_by(penholodigitals,1,3)):"\n"),

{is,s} = iff(count=1?{"is",""}:{"are","s"})

printf(1,"There %s %d penholodigital%s in base %d%s\n",{is,count,s,base,p})

end procedure

integer lim = iff(platform()=JS?14: -- ~18s

iff(machine_bits()=32?15 -- (initial square(16) is 4 out)

:16)) -- ~7.5 mins (ho hum)

papply(tagset(lim,2),penholodigital)

<pre>

There is 1 penholodigital in base 2:

1**2 = 1

There are 0 penholodigitals in base 3

There are 0 penholodigitals in base 4

There are 0 penholodigitals in base 5

There are 2 penholodigitals in base 6:

122**2 = 15324 221**2 = 53241

There is 1 penholodigital in base 7:

645**2 = 623514

There is 1 penholodigital in base 8:

2453**2 = 6532471

There are 10 penholodigitals 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 penholodigitals 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 penholodigitals 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 penholodigitals 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 0 penholodigitals in base 13

There are 160 penholodigitals in base 14:

1129535**2 = 126A84D79C53B .. 3A03226**2 = DB3962A7541C8

There are 419 penholodigitals in base 15:

4240C58**2 = 12378DA5B6EC94 .. EE25E4A**2 = ED4C93285671BA

There are 740 penholodigitals in base 16:

11156EB6**2 = 123DA7F85BCE964 .. 3FD8F786**2 = FEC81B69573DA24

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=={{header|Raku}}==