A137113 Numbers k such that k and k^2 use only the digits 2, 5, 6 and 8.

5, 25, 2585, 828665, 25662585

Offset

1,1

Comments

Generated with DrScheme.

No further terms < 2*10^22. - Robert Israel, Oct 04 2019

No further terms < 10^29. - David A. Corneth, Oct 04 2019

From Pontus von Brömssen, May 01 2024: (Start)

a(6) > 2*10^42 (if it exists).

If k = x*10^m is a term where 1 < x < 10, then 2.285225552658255282822286652822882258655265 < x < 8.286665688252826268282222255552586655885823.

(End)

Links

Table of n, a(n) for n=1..5.

J. Wellons, Tables of Shared Digits [Wayback Machine link added by Felix Fröhlich, Oct 04 2019]

Example

25662585^2 = 658568268882225.

Maple

Extend:= proc(x, d)
local i;
  op(select(t -> member(floor(t^2/10^(d)) mod 10, {2, 5, 6, 8}), [seq(i*10^d+x, i=[2, 5, 6, 8])]))
end proc:
R[0]:= [5, 6]:
for m from 1 to 10 do R[m]:= map(Extend, R[m-1], m) od:
[seq(op(select(t -> convert(convert(t^2, base, 10), set) subset {2, 5, 6, 8}, R[m])), m=0..10)]; # Robert Israel, Oct 04 2019

Mathematica

With[{c={2, 5, 6, 8}}, Select[FromDigits/@Flatten[Table[Tuples[c, n], {n, 8}], 1], SubsetQ[ c, IntegerDigits[#^2]]&]] (* Harvey P. Dale, Jan 25 2021 *)

Prog

(Magma) [k:k in [1..10^6]| Set(Intseq(k)) join Set(Intseq(k^2)) subset {2, 5, 6, 8}]; // Marius A. Burtea, Oct 04 2019
(PARI) is(n) = my(v=[0, 1, 3, 4, 7, 9]); #setintersect(vecsort(digits(n), , 8), v)==0 && #setintersect(vecsort(digits(n^2), , 8), v)==0 \\ Felix Fröhlich, Oct 04 2019

Crossrefs

Sequence in context: A328124 A033981 A099077 * A137115 A060063 A106295

Adjacent sequences: A137110 A137111 A137112 * A137114 A137115 A137116

Keyword

nonn,base,more

Author

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

Status

approved