%I #18 May 10 2024 10:59:46
%S 5,6,25,235,256,23566,2352365325,23523653335
%N Numbers k such that k and k^2 use only the digits 2, 3, 5 and 6.
%C Generated with DrScheme.
%C No more terms < 10^26. - _Robert Israel_, Nov 24 2023
%H Jonathan Wellons, <a href="https://web.archive.org/web/20090206165028/http://jonathanwellons.com/shared-digits/">Tables of Shared Digits</a> [archived]
%e 2352365325^2 = 5533622622262355625.
%p Good := {2, 3, 5, 6}: R:= 5, 6:
%p G[1]:= {5, 6}:
%p for d from 2 to 26 do
%p G[d]:= select(t -> member(floor((t^2 mod 10^d)/10^(d-1)), Good), map(t -> seq(10^(d-1)*i+t, i=Good), G[d-1]));
%p for t in G[d] do
%p if convert(convert(t^2, base, 10), set) subset Good then R:= R, t fi
%p od od:
%p sort([R]); # _Robert Israel_, Nov 24 2023
%t fQ[n_] := Block[{d = DigitCount@ n}, Total@ Delete[d, {{2}, {3}, {5}, {6}}] == 0]; Select[Range@ 100000, fQ@ # && fQ[#^2] &] (* _Michael De Vlieger_, Apr 29 2015 *)
%o (Python)
%o from itertools import product
%o A137079_list = [int(''.join(a)+b) for l in range(10) for a in product('2356',repeat = l) for b in ('5','6') if set(str(int(''.join(a)+b)**2)) <= {'2','3','5','6'}]
%o # _Chai Wah Wu_, Apr 29 2015
%K base,nonn,more
%O 1,1
%A Jonathan Wellons (wellons(AT)gmail.com), Jan 22 2008