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 A321321 #12 Jun 14 2019 04:02:31 %S A321321 1,3,5,6,7,9,11,12,13,14,17,19,21,24,25,28,31,33,35,37,41,42,48,49,56, %T A321321 65,67,69,73,81,87,96,97,112,129,131,133,137,145,161,167,192,193,224, %U A321321 257,259,261,265,273,289,321,384,385,448,513,515,517,521,529,545 %N A321321 Numbers n for which the "partition-and-add" operation applied to the binary representation of n results in only one power of 2. %C A321321 Conjecture: With the exception of a(1) = 1 and a(17) = 31, all terms have a binary weight of 2 or 3. - _Peter Kagey_, Jun 14 2019 %H A321321 Peter Kagey, <a href="/A321321/b321321.txt">Table of n, a(n) for n = 1..200</a> %H A321321 E. Berlekamp, J. Buhler, <a href="http://www.msri.org/attachments/media/news/emissary/EmissaryFall2011.pdf">Puzzle 6</a>, Puzzles column, Emissary Fall (2011) 9. %H A321321 Steve Butler, Ron Graham, and Richard Stong, <a href="http://www.math.ucsd.edu/~ronspubs/mis_17_bases.pdf">Collapsing numbers in bases 2, 3, and beyond</a>, in The Proceedings of the Gathering for Gardner 10 (2012). %H A321321 Steve Butler, Ron Graham, and Richard Strong, <a href="http://orion.math.iastate.edu/butler/papers/16_03_insert_and_add.pdf">Inserting plus signs and adding</a>, Amer. Math. Monthly 123 (3) (2016), 274-279. %e A321321 For n = 13, we can partition its binary representation as follows (showing partition and sum of terms): (1101):13, (1)(101):6, (11)(01):4, (110)(1):7, (1)(1)(01):3, (1)(10)(1):4, (11)(0)(1):4, (1)(1)(0)(1):3. Thus there is only one possible power of 2, namely 4. %Y A321321 Cf. A321318, A321319, A321320. %K A321321 nonn %O A321321 1,2 %A A321321 _Jeffrey Shallit_, Nov 04 2018