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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 October 14 12:02 EDT 2019. Contains 328004 sequences. (Running on oeis4.)