|
| |
|
|
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
|
|
|
|
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)]]];
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
