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

1,2

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

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

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.

Sequence in context: A103097 A335750 A062286 * A354014 A195729 A303950

Adjacent sequences: A071068 A071069 A071070 * A071072 A071073 A071074

Keyword

fini,full,nonn,base

Author

Benoit Cloitre, May 26 2002

Status

approved