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 A321320 #11 Nov 04 2018 20:36:24 %S A321320 1,2,2,4,2,2,4,8,2,4,4,2,4,4,8,16,2,4,4,4,4,8,8,2,4,8,8,4,8,8,16,32,2, %T A321320 4,4,8,4,8,8,4,4,4,8,8,8,16,16,2,4,8,8,8,8,8,16,4,8,16,16,8,16,16,32, %U A321320 64,2,4,4,8,4,8,8,8,4,8,8,16,8,16,16,4,4,8 %N A321320 Largest power of 2 obtainable by partitioning the binary representation of n into consecutive blocks and then summing. %H A321320 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 A321320 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. %H A321320 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). %e A321320 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 the largest power of 2 is 4. %Y A321320 Cf. A321318, A321319, A321321. %K A321320 nonn %O A321320 1,2 %A A321320 _Jeffrey Shallit_, Nov 04 2018