%N Minimal "powers of 2" set in base 10: any power of 2 contains at least one term of this sequence in its decimal expansion.
%C Conjectured by J. Shallit to be complete.
%C 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
%D J.-P. Delahaye, Nombres premiers inévitables et pyramidaux, Pour la science, (French edition of Scientific American), Juin 2002, p. 98
%H Bassam Abdul-Baki, <a href="/A071071/a071071.pdf">Minimal Sets for Powers of 2</a>
%H David Butler, <a href="https://blogs.adelaide.edu.au/maths-learning/2017/06/21/65536/">65536</a>, Making Your Own Sense, June 21 2017.
%H Jeffrey Shallit, <a href="http://recursed.blogspot.com/2006/12/prime-game.html">The Prime Game</a>, Recursivity, December 01 2006.
%H <a href="/index/Di#divseq">Index to divisibility sequences</a>
%Y Cf. A071062, A071070, A071072, A071073.
%A _Benoit Cloitre_, May 26 2002