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A308746
a(1) = 1, and for n > 1, a(n) is the greatest k > 0 such that (a(1), ..., a(n-1)) can be split into k chunks of contiguous terms and those chunks have the same sum.
2
1, 1, 2, 2, 3, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 2, 4, 2, 5, 1, 6, 7, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 2, 4, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 5, 1, 1, 1, 2, 2, 2, 2, 2, 6, 2, 2, 2, 4, 2, 7, 1, 2, 2, 2, 2, 1, 1, 8, 2, 2, 3, 3, 9, 3, 3, 3, 10, 2, 2, 2
OFFSET
1,3
COMMENTS
For any n > 0, a(n) divides Sum_{k = 1..n-1} a(k).
Is this sequence unbounded?
LINKS
Rémy Sigrist, Colored scatterplot of the first 1000000 terms (where the color is function of Sum_{k = 1..n-1} a(k) / a(n))
EXAMPLE
The first terms, alongside the corresponding chunks, are:
n a(n) Chunks (separated by pipes)
-- ---- -------------------------------------
1 1
2 1 1
3 2 1|1
4 2 1 1|2
5 3 1 1|2|2
6 1 1 1 2 2 3
7 1 1 1 2 2 3 1
8 1 1 1 2 2 3 1 1
9 2 1 1 2 2|3 1 1 1
10 1 1 1 2 2 3 1 1 1 2
11 1 1 1 2 2 3 1 1 1 2 1
12 1 1 1 2 2 3 1 1 1 2 1 1
13 1 1 1 2 2 3 1 1 1 2 1 1 1
14 3 1 1 2 2|3 1 1 1|2 1 1 1 1
15 1 1 1 2 2 3 1 1 1 2 1 1 1 1 3
16 2 1 1 2 2 3 1 1|1 2 1 1 1 1 3 1
17 4 1 1 2 2|3 1 1 1|2 1 1 1 1|3 1 2
18 2 1 1 2 2 3 1 1 1 2|1 1 1 1 3 1 2 4
19 5 1 1 2 2|3 1 1 1|2 1 1 1 1|3 1 2|4 2
20 1 1 1 2 2 3 1 1 1 2 1 1 1 1 3 1 2 4 2 5
PROG
(PARI) See Links section.
CROSSREFS
Cf. A095258.
Sequence in context: A084352 A106797 A329311 * A367125 A074313 A367438
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Jun 21 2019
STATUS
approved