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 A364650 #4 Aug 02 2023 13:50:36 %S A364650 1,2,1,1,1,3,0,1,1,1,2,0,1,3,1,1,2,1,1,1,0,1 %N A364650 Number of powers of 3 whose binary representation contains exactly n 1's. %C A364650 Number of numbers k >= 0 such that A011754(k) = n. %C A364650 Senge and Straus prove that a(n) is finite for all n. %C A364650 After a(22), the sequence undoubtedly continues 0, 1, 3, 2, 1, 1, 1, 1, 0, 2, 1, 4, 1, 1, 0, 2, 4, 1, 2, 3, 0, 0, 2, 1, 1, 1, 1, 0, ..., but there seem to be proofs only for the first 22 terms (Dimitrov and Howe). %H A364650 Vassil S. Dimitrov and Everett W. Howe, <a href="https://arxiv.org/abs/2105.06440">Powers of 3 with few nonzero bits and a conjecture of Erdős</a>, arXiv:2105.06440 [math.NT], 2021. %H A364650 H. G. Senge and E. G. Straus, <a href="https://doi.org/10.1007/BF02018464">PV-numbers and sets of multiplicity</a>, Periodica Mathematica Hungarica 3 (1973), 93-100. %e A364650 There are a(6) = 3 powers of 3 that have exactly 6 binary 1's: 3^5 (11110011 in binary), 3^6 (1011011001), and 3^8 (1100110100001). %e A364650 There is no power of 3 with exactly 7 binary 1's, so a(7) = 0. %Y A364650 Cf. A011754. %K A364650 nonn,base,more %O A364650 1,2 %A A364650 _Pontus von Brömssen_, Jul 31 2023