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

1,2

Comments

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

Links

Table of n, a(n) for n=1..82.

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

Example

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.

Crossrefs

Cf. A163169, A003059, A064816, A118139

Sequence in context: A107325 A003050 A070868 * A272612 A155216 A064144

Adjacent sequences: A342216 A342217 A342218 * A342220 A342221 A342222

Keyword

nonn

Author

Scott R. Shannon, Mar 05 2021

Status

approved