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A137105 Numbers k such that k and k^2 use only the digits 2, 4, 6 and 9.

%I A137105 #9 Apr 12 2024 09:51:27
%S A137105 2,264,964,494262,494462,4946662,4996962,49944662,499466662,
%T A137105 49994666662,49999296962,499999296962,4999946666662,499999466666662,
%U A137105 49999994666666662,4999999946666666662,499999999466666666662,49999999994666666666662,4999999999946666666666662,499999999999466666666666662
%N A137105 Numbers k such that k and k^2 use only the digits 2, 4, 6 and 9.
%C A137105 Generated with DrScheme.
%C A137105 Includes 5*10^(2*k) - (16*10^k + 14)/3 for k >= 3. The only terms < 10^28 not of that form are 2, 264, 964, 494262, 494462, 4996962, 49944662, 49999296962, and 499999296962. - _Robert Israel_, Nov 24 2023
%H A137105 J. Wellons, <a href="https://web.archive.org/web/20090206165028/http://jonathanwellons.com/shared-digits/">Tables of Shared Digits</a> [archived]
%e A137105 499999296962^2 = 249999296962494262429444.
%p A137105 Good := {2, 4, 6, 9}: R:= 2:
%p A137105 G[1]:= {2, 4, 6}:
%p A137105 for d from 2 to 28 do
%p A137105   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 A137105   for t in G[d] do
%p A137105     if convert(convert(t^2, base, 10), set) subset Good then  R:= R, t fi
%p A137105 od od:
%p A137105 sort([R]); # _Robert Israel_, Nov 24 2023
%K A137105 base,nonn
%O A137105 1,1
%A A137105 Jonathan Wellons (wellons(AT)gmail.com), Jan 22 2008
%E A137105 More terms from _Robert Israel_, Nov 24 2023