

A102483


Numbers k such that 2^k contains no zeros in base 3.


18




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

Table of n, a(n) for n=1..6.
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), 9798.
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

Cf. A007377, A004642, A346497.
Sequence in context: A295756 A140047 A297840 * A134916 A085100 A337117
Adjacent sequences: A102480 A102481 A102482 * A102484 A102485 A102486


KEYWORD

nonn,base,hard


AUTHOR

N. J. A. Sloane, Feb 25 2005


STATUS

approved



