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

2, 3, 4943, 499423, 49993443, 4999932923, 499999999293429243923, 499999999999293429243923

Offset: 1

Author

Jonathan Wellons (wellons(AT)gmail.com), Jan 22 2008

Keywords

• base
• nonn
• more

Comments

Generated with DrScheme.

Examples

			4999932923^2 = 24999329234499323929.
		

Links

• Jonathan Wellons, Tables of Shared Digits [archived]

Crossrefs

Cf. A136809.

Programs

Maple

g:= n -> convert(convert(n,base,10),set) subset {2,3,4,9}:
Res:= 2,3:
extend:= proc(n,d) local B; global Res;
B:= {seq(x*10^d+n,x=[2,3,4,9])};
Res:= Res, op(select(t -> g(t^2), B));
op(select(t -> g(t^2 mod 10^(d+1)), B))
end proc:
Agenda:= {2,3,4,9}:
for d from 1 to 25 do Agenda:= map(extend,Agenda,d) od:
sort([Res]); # Robert Israel, Oct 29 2018

Extensions

a(7)-a(8) from Andrew Howroyd, Oct 24 2018