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 A306922 #20 Jun 14 2019 21:25:46 %S A306922 1,2,1,3,1,1,1,4,1,2,1,1,1,1,2,5,1,2,1,2,1,2,2,1,1,2,2,1,2,2,1,6,1,2, %T A306922 1,3,1,2,2,2,1,1,2,2,2,3,2,1,1,2,2,2,2,2,2,1,2,3,2,2,2,2,2,7,1,2,1,3, %U A306922 1,2,2,3,1,2,2,3,2,3,2,2,1,2,2,2,2,3,1 %N A306922 Number of distinct powers of two obtained by breaking the binary representation of n into consecutive blocks, and then adding the numbers represented by the blocks. %C A306922 1's appear at indices given by A321321. %H A306922 Peter Kagey, <a href="/A306922/b306922.txt">Table of n, a(n) for n = 1..10000</a> %H A306922 Elwyn Berlekamp and Joe P. Buhler, <a href="http://www.msri.org/attachments/media/news/emissary/EmissaryFall2011.pdf">Puzzle 6</a>, Puzzles column, Emissary, MSRI Newsletter, Fall 2011, Page 9, Problem 6. %H A306922 Reddit user HarryPotter5777, <a href="https://www.reddit.com/r/mathriddles/comments/b1ixi9/partition_a_binary_string_so_sum_of_chunks_is_a/ein7qef/">Partition a binary string so sum of chunks is a power of two</a>. (Proposed proof that a(n) > 0 for all n.) %e A306922 For n = 46, the a(46) = 3 powers of two that come from the partition of "101110" are 4, 8, and 16: %e A306922 [10, 1110] -> [2, 14] -> 16 %e A306922 [1, 0, 1, 110] -> [1, 0, 1, 6] -> 8 %e A306922 [101, 1, 10] -> [5, 1, 2] -> 8 %e A306922 [1, 0, 111, 0] -> [1, 0, 7, 0] -> 8 %e A306922 [101, 11, 0] -> [5, 3, 0] -> 8 %e A306922 [1, 0, 1, 1, 1, 0] -> [1, 0, 1, 1, 1, 0] -> 4 %Y A306922 Cf. A306921, A321318, A321319, A321320, A321321. %K A306922 nonn,base %O A306922 1,2 %A A306922 _Peter Kagey_, Mar 16 2019