This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A346497 #49 Feb 18 2025 14:41:15
%S A346497 1,2,11,22,121,1122221122
%N A346497 List of powers of 2 written in base 3 which contain no zero digits.
%C A346497 The listed terms are the base-3 expansions of 1, 2, 4, 8, 16, and 32768.
%C A346497 The program shows that there are no other terms less than 2^1000.
%C A346497 a(7) > 2^(10^7). - _Martin Ehrenstein_, Jul 27 2021
%C A346497 If it exists, a(7) > 2^(10^21). - _Robert Saye_, Mar 23 2022
%D A346497 David Wells, "The Penguin Dictionary of Curious and Interesting Numbers" (1997), p. 123.
%H A346497 R. C. Couto, <a href="https://codepen.io/rafaelcastrocouto/pen/jOmwxQj">Number of nonzero digits in 2^n base 3</a>
%H A346497 Robert I. Saye, <a href="https://arxiv.org/abs/2202.13256">On two conjectures concerning the ternary digits of powers of two</a>, arXiv:2202.13256 [math.NT], 2022; J. Integer Seq. 25 (2022) Article 22.3.4.
%F A346497 a(n) = A007089(2^A102483(n)). - _Michel Marcus_, Jul 23 2021
%t A346497 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 *)
%t A346497 Select[Table[FromDigits[IntegerDigits[2^n,3]],{n,0,100}],DigitCount[#,10,0]==0&] (* _Harvey P. Dale_, Feb 18 2025 *)
%Y A346497 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).
%K A346497 nonn,base,hard,more
%O A346497 1,2
%A A346497 _Rafael Castro Couto_, Jul 20 2021