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 A321318 Number of distinct values obtained by partitioning the binary representation of n into consecutive blocks, and then summing the numbers represented by the blocks. 3
 1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 8, 8, 7, 7, 9, 9, 8, 8, 7, 7, 6, 6, 9, 9, 9, 9, 10, 10, 9, 9, 9, 9, 12, 12, 13, 13, 9, 9, 12, 12, 12, 12, 12, 12, 12, 12, 14, 14, 12, 12, 11, 11, 7, 7, 11, 11, 12, 12, 13, 13, 12, 12, 15, 15, 15 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Elwyn Berlekamp and Joe P. Buhler, Puzzle 6, Puzzles column, Emissary, MSRI Newsletter, Fall 2011, Page 9, Problem 6. 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 there are 5 distinct values. CROSSREFS Cf. A321319, A321320, A321321. Sequence in context: A093875 A266193 A114214 * A270362 A196383 A074198 Adjacent sequences:  A321315 A321316 A321317 * A321319 A321320 A321321 KEYWORD nonn AUTHOR Jeffrey Shallit, Nov 04 2018 STATUS approved

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Last modified February 18 20:12 EST 2019. Contains 320262 sequences. (Running on oeis4.)