[go: up one dir, main page]

login
A346497
List of powers of 2 written in base 3 which contain no zero digits.
3
1, 2, 11, 22, 121, 1122221122
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
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
a(n) = A007089(2^A102483(n)). - Michel Marcus, Jul 23 2021
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
Cf. A102483, A004642 (all powers of 2 in base 3), A104320 (number of zeros in ternary representation of 2^n), A130693 (same problem in base 10).
Sequence in context: A376688 A018351 A004642 * A185545 A001032 A045386
KEYWORD
nonn,base,hard,more
AUTHOR
Rafael Castro Couto, Jul 20 2021
STATUS
approved