A071071 Minimal "powers of 2" set in base 10: any power of 2 contains at least one term of this sequence in its decimal expansion.

1, 2, 4, 8, 65536

Offset: 1

Author

Benoit Cloitre, May 26 2002

Keywords

• fini
• full
• nonn
• base

Comments

Conjectured by J. Shallit to be complete.

A possible exception are powers of 16. It can be proved that 16^(5^(k-1) + floor((k+3)/4)) == 16^floor((k+3)/4) (mod 10^k) (see attached proof). Thus it may be that there is a power of 16 that does not contain any of the digits 1, 2, 4, and 8 or the number 65536 as a substring. - Bassam Abdul-Baki, Apr 10 2019

References

• J.-P. Delahaye, Nombres premiers inévitables et pyramidaux, Pour la science, (French edition of Scientific American), Juin 2002, p. 98

Links

• Bassam Abdul-Baki, Minimal Sets for Powers of 2
• David Butler, 65536, Making Your Own Sense, June 21 2017.
• Jeffrey Shallit, The Prime Game, Recursivity, December 01 2006.
• Index to divisibility sequences

Crossrefs

Cf. A071062, A071070, A071072, A071073.