OFFSET
1,2
COMMENTS
The listed terms are the base-3 expansions of 1, 2, 4, 8, 16, and 32768.
The program shows that there are no other terms less than 2^1000.
a(7) > 2^(10^7). - Martin Ehrenstein, Jul 27 2021
If it exists, a(7) > 2^(10^21). - Robert Saye, Mar 23 2022
REFERENCES
David Wells, "The Penguin Dictionary of Curious and Interesting Numbers" (1997), p. 123.
LINKS
R. C. Couto, Number of nonzero digits in 2^n base 3
Robert I. Saye, On two conjectures concerning the ternary digits of powers of two, arXiv:2202.13256 [math.NT], 2022; J. Integer Seq. 25 (2022) Article 22.3.4.
FORMULA
MATHEMATICA
pwr = 1; Do[pwr = Mod[2*pwr, 3^100]; d = Union[IntegerDigits[pwr, 3]]; If[Intersection[d, {0}] == {}, Print[IntegerString[pwr, 3]]], {n, 10000000}] (* Ricardo Bittencourt, Jul 07 2021 *)
CROSSREFS
KEYWORD
nonn,base,hard,more
AUTHOR
Rafael Castro Couto, Jul 20 2021
STATUS
approved