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 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. 7
 1, 2, 4, 8, 65536 (list; graph; refs; listen; history; text; internal format)
 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 inĂ©vitables 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. CROSSREFS Cf. A071062, A071070, A071072, A071073. Sequence in context: A103097 A335750 A062286 * A195729 A303950 A011181 Adjacent sequences:  A071068 A071069 A071070 * A071072 A071073 A071074 KEYWORD fini,full,nonn,base AUTHOR Benoit Cloitre, May 26 2002 STATUS approved

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Last modified August 12 08:51 EDT 2020. Contains 336438 sequences. (Running on oeis4.)