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
KEYWORD
fini,full,nonn,base
AUTHOR
Benoit Cloitre, May 26 2002
STATUS
approved