|
%I #33 Mar 18 2023 08:49:14
%S 0,1,2,3,4,15
%N Numbers k such that 2^k contains no zeros in base 3.
%C I conjectured in 1973 that there are no further terms. This question is still open.
%C A104320(a(n)) = 0. - _Reinhard Zumkeller_, Mar 01 2005
%C No other terms less than 200000. - _Robert G. Wilson v_, Dec 06 2005
%C a(7) > 10^7. - _Martin Ehrenstein_, Jul 27 2021
%C If it exists, a(7) > 10^21. - _Robert Saye_, Mar 23 2022
%H Robert I. Saye, <a href="https://arxiv.org/abs/2202.13256">On two conjectures concerning the ternary digits of powers of two</a>, J. Integer Seq. 25 (2022) Article 22.3.4.
%H N. J. A. Sloane, <a href="http://neilsloane.com/doc/persistence.html">The persistence of a number</a>, J. Recreational Math., 6 (1973), 97-98.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Ternary.html">Ternary</a>
%t Select[ Range@1000, FreeQ[ IntegerDigits[2^#, 3], 0] &] (* _Robert G. Wilson v_, Dec 06 2005 *)
%o (PARI) for (n=0, 100, if (vecmin(digits(2^n, 3)), print1(n, ", "))) \\ _Michel Marcus_, Mar 25 2015
%Y Cf. A007377, A004642, A346497.
%K nonn,base,hard
%O 1,3
%A _N. J. A. Sloane_, Feb 25 2005
|
