A338774 a(n) is the greatest k such that 0 <= k < n and the k latest terms so far sum up to a square number.

0, 1, 2, 0, 1, 5, 6, 0, 1, 9, 10, 0, 1, 13, 14, 0, 1, 17, 18, 8, 0, 1, 3, 3, 0, 1, 19, 0, 1, 18, 24, 0, 1, 27, 28, 18, 16, 1, 19, 3, 38, 36, 39, 40, 0, 1, 43, 44, 0, 1, 47, 48, 0, 1, 51, 52, 16, 1, 7, 0, 1, 13, 21, 39, 34, 38, 64, 62, 65, 66, 43, 40, 63, 19

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 A338774

Formula

a(n) < n.

Example

The first terms, alongside the corresponding squares, are:
  n   a(n)  Corresponding squares (A338780(n)^2)
  --  ----  ------------------------------------
   1     0                      0^2 (empty sum)
   2     1                  0 = 0^2
   3     2                0+1 = 1^2
   4     0                      0^2 (empty sum)
   5     1                  0 = 0^2
   6     5          0+1+2+0+1 = 2^2
   7     6        0+1+2+0+1+5 = 3^2
   8     0                      0^2 (empty sum)
   9     1                  0 = 0^2
  10     9  0+1+2+0+1+5+6+0+1 = 4^2

Prog

(PARI) See Links section.

Crossrefs

See A338773 for a similar sequence.

Cf. A338780.

Sequence in context: A094456 A010028 A151860 * A330891 A089627 A306534

Adjacent sequences: A338771 A338772 A338773 * A338775 A338776 A338777

Keyword

nonn

Author

Rémy Sigrist, Nov 08 2020

Status

approved