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

Offset: 1

Author

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

Keywords

• base
• nonn

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

Examples

			499999296962^2 = 249999296962494262429444.
		

Links

• J. Wellons, Tables of Shared Digits [archived]

Programs

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
od od:
sort([R]); # Robert Israel, Nov 24 2023

Extensions

More terms from Robert Israel, Nov 24 2023