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A071071
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Minimal "powers of 2" set in base 10: any power of 2 contains at least one term of this sequence in its decimal expansion.
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8
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OFFSET
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1,2
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COMMENTS
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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
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REFERENCES
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J.-P. Delahaye, Nombres premiers inévitables et pyramidaux, Pour la science, (French edition of Scientific American), Juin 2002, p. 98
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LINKS
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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
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CROSSREFS
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Cf. A071062, A071070, A071072, A071073.
Sequence in context: A103097 A335750 A062286 * A354014 A195729 A303950
Adjacent sequences: A071068 A071069 A071070 * A071072 A071073 A071074
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KEYWORD
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fini,full,nonn,base
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AUTHOR
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Benoit Cloitre, May 26 2002
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STATUS
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approved
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