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 A321319 Smallest power of 2 obtainable by partitioning the binary representation of n into consecutive blocks and then summing. 4
 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, 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, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 8, 2, 4, 4, 4, 4, 4, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS E. Berlekamp, J. Buhler, Puzzle 6, Puzzles column, Emissary Fall (2011) 9. Steve Butler, Ron Graham, and Richard Stong, Collapsing numbers in bases 2, 3, and beyond, in The Proceedings of the Gathering for Gardner 10 (2012). Steve Butler, Ron Graham, and Richard Strong, Inserting plus signs and adding, Amer. Math. Monthly 123 (3) (2016), 274-279. EXAMPLE 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. CROSSREFS Cf. A321318, A321320, A321321. Sequence in context: A255723 A309022 A214718 * A048896 A130831 A151678 Adjacent sequences:  A321316 A321317 A321318 * A321320 A321321 A321322 KEYWORD nonn AUTHOR Jeffrey Shallit, Nov 04 2018 STATUS approved

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Last modified May 10 21:08 EDT 2021. Contains 343780 sequences. (Running on oeis4.)