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 A256504 Summative Fission - For a positive integer n, find the greatest number of consecutive positive integers (at least 2) which add to n. For each of these do the same ... iterate to completion. a(n) = the total number of integers (including n itself) defined. 1
 0, 1, 1, 3, 1, 5, 6, 5, 1, 6, 7, 12, 10, 12, 11, 12, 1, 8, 16, 14, 17, 18, 18, 23, 13, 21, 18, 22, 23, 24, 19, 14, 1, 22, 20, 23, 24, 31, 27, 25, 26, 36, 28, 37, 29, 30, 42, 37, 22, 32, 37, 38, 35, 41, 36, 37, 43, 42, 37, 44, 44, 34, 33, 47, 1, 48, 49, 43, 53 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS The iteration that leads to this sequence is worthy of consideration for the grade 2 classroom learning addition. a(2^k)=1 for all nonnegative integers k as can be seen from A138591. LINKS Martin Büttner, Table of n, a(n) for n = 0..10000 EXAMPLE a(23) = 23 because there are 23 numbers generated by the iteration:                   23                   /\                  /  \                 /    \                /      \               /        \              /          \             /            \           11             12           /\             /|\          /  \           / | \         /    \         /  |  \        /      \       3   4   5       /        \     / \     / \      5          6   1   2   2   3     / \        /|\             / \    2   3      / | \           1   2       / \    /  |  \      1   2  1   2   3                    / \                   1   2 a(24) = 13 because there are 13 numbers generated by the iteration:           24           /|\          / | \         /  |  \        7   8   9       / \     /|\      3   4   / | \     / \     /  |  \    1   2   2   3   4               / \              1   2 MATHEMATICA fission[0] = 0; fission[n_] := fission@n = Module[{div = SelectFirst[Reverse@Divisors[2 n], (OddQ@# == IntegerQ[n/#] && n/# > (# - 1)/2) &]}, If[div == 1, 1, 1 + Total[fission /@ (Range@div + n/div - (div + 1)/2)]]]; fission /@ Range[0, 100] (* Martin Büttner, Jun 04 2015 *) CROSSREFS Cf. A138591. Sequence in context: A208904 A209754 A140950 * A205713 A254344 A278032 Adjacent sequences:  A256501 A256502 A256503 * A256505 A256506 A256507 KEYWORD nonn,easy AUTHOR Gordon Hamilton, Mar 31 2015 EXTENSIONS Corrected and extended by Martin Büttner, Jun 04 2015 STATUS approved

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Last modified April 18 01:48 EDT 2021. Contains 343072 sequences. (Running on oeis4.)