A338773 a(n) is the number of distinct k such that 0 < k < n and a(k) + ... + a(n-1) is a square number.

0, 1, 2, 0, 1, 4, 1, 3, 3, 0, 1, 5, 1, 1, 1, 4, 4, 3, 0, 1, 5, 2, 0, 1, 6, 2, 6, 2, 4, 6, 1, 4, 2, 3, 4, 6, 2, 3, 1, 8, 3, 4, 3, 1, 5, 5, 2, 1, 4, 4, 7, 5, 3, 2, 4, 4, 4, 4, 5, 2, 4, 3, 1, 7, 3, 2, 8, 5, 2, 4, 4, 6, 7, 6, 2, 9, 4, 6, 4, 2, 6, 4, 5, 6, 2, 3, 5

Offset

1,3

Comments

If a(n) = 0, then a(n+1) = 1 and a(n+2) >= 2.

Links

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

Rémy Sigrist, PARI program for A338773

Example

The first terms, alongside the corresponding k's, are:
  n   a(n)  Corresponding k's
  --  ----  -----------------
   1     0  {}
   2     1  {1}
   3     2  {1, 2}
   4     0  {}
   5     1  {4}
   6     4  {1, 2, 4, 5}
   7     1  {6}
   8     3  {1, 2, 7}
   9     3  {4, 5, 7}
  10     0  {}

Prog

(PARI) See Links section.

Crossrefs

See A338774 for a similar sequence.

Sequence in context: A121583 A228924 A246862 * A194686 A302996 A266213

Adjacent sequences: A338770 A338771 A338772 * A338774 A338775 A338776

Keyword

nonn

Author

Rémy Sigrist, Nov 08 2020

Status

approved