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A137078 Numbers k such that k and k^2 use only the digits 2, 3, 4 and 9.

%I A137078 #20 May 10 2024 10:59:42
%S A137078 2,3,4943,499423,49993443,4999932923,499999999293429243923,
%T A137078 499999999999293429243923
%N A137078 Numbers k such that k and k^2 use only the digits 2, 3, 4 and 9.
%C A137078 Generated with DrScheme.
%H A137078 Jonathan Wellons, <a href="https://web.archive.org/web/20090206165028/http://jonathanwellons.com/shared-digits/">Tables of Shared Digits</a> [archived]
%e A137078 4999932923^2 = 24999329234499323929.
%p A137078 g:= n -> convert(convert(n,base,10),set) subset {2,3,4,9}:
%p A137078 Res:= 2,3:
%p A137078 extend:= proc(n,d) local B; global Res;
%p A137078 B:= {seq(x*10^d+n,x=[2,3,4,9])};
%p A137078 Res:= Res, op(select(t -> g(t^2), B));
%p A137078 op(select(t -> g(t^2 mod 10^(d+1)), B))
%p A137078 end proc:
%p A137078 Agenda:= {2,3,4,9}:
%p A137078 for d from 1 to 25 do Agenda:= map(extend,Agenda,d) od:
%p A137078 sort([Res]); # _Robert Israel_, Oct 29 2018
%Y A137078 Cf. A136809.
%K A137078 base,nonn,more
%O A137078 1,1
%A A137078 Jonathan Wellons (wellons(AT)gmail.com), Jan 22 2008
%E A137078 a(7)-a(8) from _Andrew Howroyd_, Oct 24 2018