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%I #10 Nov 04 2018 20:36:12
%S 1,1,2,1,2,2,4,1,2,2,4,2,4,4,4,1,2,2,4,2,4,4,4,2,4,4,4,4,4,4,16,1,2,2,
%T 4,2,4,4,4,2,4,4,4,4,4,4,8,2,4,4,4,4,4,4,8,4,4,4,8,4,8,8,8,1,2,2,4,2,
%U 4,4,4,2,4,4,4,4,4,4,8,2,4,4,4,4,4,4
%N Smallest power of 2 obtainable by partitioning the binary representation of n into consecutive blocks and then summing.
%H 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 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 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 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 smallest power of 2 is 4.
%Y Cf. A321318, A321320, A321321.
%K nonn
%O 1,3
%A _Jeffrey Shallit_, Nov 04 2018
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