

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
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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



