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URL: https://oeis.org/A102483

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A102483
Numbers k such that 2^k contains no zeros in base 3.
18
0, 1, 2, 3, 4, 15
OFFSET
1,3
COMMENTS
I conjectured in 1973 that there are no further terms. This question is still open.
A104320(a(n)) = 0. - Reinhard Zumkeller, Mar 01 2005
No other terms less than 200000. - Robert G. Wilson v, Dec 06 2005
a(7) > 10^7. - Martin Ehrenstein, Jul 27 2021
If it exists, a(7) > 10^21. - Robert Saye, Mar 23 2022
LINKS
Robert I. Saye, On two conjectures concerning the ternary digits of powers of two, J. Integer Seq. 25 (2022) Article 22.3.4.
N. J. A. Sloane, The persistence of a number, J. Recreational Math., 6 (1973), 97-98.
Eric Weisstein's World of Mathematics, Ternary
MATHEMATICA
Select[ Range@1000, FreeQ[ IntegerDigits[2^#, 3], 0] &] (* Robert G. Wilson v, Dec 06 2005 *)
PROG
(PARI) for (n=0, 100, if (vecmin(digits(2^n, 3)), print1(n, ", "))) \\ Michel Marcus, Mar 25 2015
CROSSREFS
KEYWORD
nonn,base,hard
AUTHOR
N. J. A. Sloane, Feb 25 2005
STATUS
approved