

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




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^(k1) + 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 AbdulBaki, 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

Table of n, a(n) for n=1..5.
Bassam AbdulBaki, 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 * A195729 A303950 A011181
Adjacent sequences: A071068 A071069 A071070 * A071072 A071073 A071074


KEYWORD

fini,full,nonn,base


AUTHOR

Benoit Cloitre, May 26 2002


STATUS

approved



