A342219 a(1) = 1, a(2) = 2; for n > 2, a(n) = the number of terms in the maximal length sum of previous consecutive terms that equals n.

1, 2, 2, 2, 3, 3, 4, 3, 4, 5, 3, 5, 6, 5, 5, 6, 7, 3, 7, 8, 7, 6, 8, 9, 7, 8, 8, 9, 10, 8, 10, 11, 8, 10, 8, 11, 12, 10, 8, 11, 10, 12, 13, 8, 12, 11, 13, 14, 11, 13, 6, 14, 15, 13, 10, 14, 9, 15, 16, 11, 14, 14, 15, 15, 16, 17, 13, 17, 18, 10, 16, 9, 17, 15, 18, 19, 16, 15, 17, 15, 18, 13

Offset: 1

Author

Scott R. Shannon, Mar 05 2021

Keywords

• nonn

Comments

The equivalent sequence for a minimal length sum is given by A003059.

Examples

			a(3) = 2 as the only way to sum previous consecutive terms to make 3 is 1 + 2 = 3, which contains two terms.
a(7) = 4 as the previous consecutive terms 1 + 2 + 2 + 2 = 7, which contains four terms. Note that 7 can also be made by consecutive terms 2 + 2 + 3 = 7, but the sequence is the maximal sum length.
a(10) = 5 as the previous consecutive terms 1 + 2 + 2 + 2 + 3 = 10, which contains five terms. Three other consecutive term sums also exist that sum to 10 but they contain fewer terms.
		

Links

• Scott R. Shannon, Scatterplot of the first 50000 terms.

Crossrefs

Cf. A163169, A003059, A064816, A118139