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A137079 Numbers k such that k and k^2 use only the digits 2, 3, 5 and 6.

%I A137079 #18 May 10 2024 10:59:46
%S A137079 5,6,25,235,256,23566,2352365325,23523653335
%N A137079 Numbers k such that k and k^2 use only the digits 2, 3, 5 and 6.
%C A137079 Generated with DrScheme.
%C A137079 No more terms < 10^26. - _Robert Israel_, Nov 24 2023
%H A137079 Jonathan Wellons, <a href="https://web.archive.org/web/20090206165028/http://jonathanwellons.com/shared-digits/">Tables of Shared Digits</a> [archived]
%e A137079 2352365325^2 = 5533622622262355625.
%p A137079 Good := {2, 3, 5, 6}: R:= 5, 6:
%p A137079 G[1]:= {5, 6}:
%p A137079 for d from 2 to 26 do
%p A137079   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 A137079   for t in G[d] do
%p A137079      if convert(convert(t^2, base, 10), set) subset Good then  R:= R, t fi
%p A137079 od od:
%p A137079 sort([R]); # _Robert Israel_, Nov 24 2023
%t A137079 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 A137079 (Python)
%o A137079 from itertools import product
%o A137079 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 A137079 # _Chai Wah Wu_, Apr 29 2015
%K A137079 base,nonn,more
%O A137079 1,1
%A A137079 Jonathan Wellons (wellons(AT)gmail.com), Jan 22 2008