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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. 8
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 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.
CROSSREFS
Sequence in context: A103097 A335750 A062286 * A354014 A195729 A303950
KEYWORD
fini,full,nonn,base
AUTHOR
Benoit Cloitre, May 26 2002
STATUS
approved

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Last modified March 29 05:48 EDT 2024. Contains 371265 sequences. (Running on oeis4.)