A137105 - OEIS

A137105

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

2, 264, 964, 494262, 494462, 4946662, 4996962, 49944662, 499466662, 49994666662, 49999296962, 499999296962, 4999946666662, 499999466666662, 49999994666666662, 4999999946666666662, 499999999466666666662, 49999999994666666666662, 4999999999946666666666662, 499999999999466666666666662

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OFFSET

1,1

COMMENTS

Generated with DrScheme.

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

LINKS

Table of n, a(n) for n=1..20.

J. Wellons, Tables of Shared Digits [archived]

EXAMPLE

499999296962^2 = 249999296962494262429444.

MAPLE

Good := {2, 4, 6, 9}: R:= 2:

G[1]:= {2, 4, 6}:

for d from 2 to 28 do

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]));

for t in G[d] do

if convert(convert(t^2, base, 10), set) subset Good then R:= R, t fi