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.

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, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Colored scatterplot of the first 1000000 terms (where the color is function of Sum_{k = 1..n-1} a(k) / a(n))

Rémy Sigrist, PARI program for A308746

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

Adjacent sequences: A308743 A308744 A308745 * A308747 A308748 A308749

Keyword

nonn

Author

Rémy Sigrist, Jun 21 2019

Status

approved