A359634 a(0)=1 and thereafter a(n) is the length of the longest contiguous group of terms in the sequence thus far that add up to n; if no such group exists, set a(n)=0.

1, 1, 2, 2, 3, 3, 4, 3, 4, 5, 4, 5, 6, 4, 5, 6, 7, 6, 7, 8, 5, 7, 8, 9, 7, 6, 8, 9, 10, 6, 9, 10, 11, 9, 8, 10, 11, 12, 9, 10, 9, 11, 12, 13, 7, 12, 13, 14, 12, 11, 13, 14, 15, 11, 13, 11, 14, 15, 16, 13, 6, 14, 13, 15, 16, 17, 13, 15, 12, 16, 17, 18, 15, 8, 16, 14, 17, 18, 19, 15, 16, 12, 17, 14, 18, 19, 20

Offset: 0

Author

Neal Gersh Tolunsky, Jan 08 2023

Keywords

• nonn

Comments

If a zero appears, it is not counted as a term in a contiguous grouping. For example, if (10, 30, 0, 60) is our longest group to sum to 100, this counts as 3 terms, not 4. However, in 50 million terms (computed by Kevin Ryde), a zero has not appeared. Why is this?

How does the lower envelope of this sequence behave?

Examples

			a(6) is 4 because in the sequence thus far (1,1,2,2,3,3), the longest run of consecutive terms that sums to 6 is (1,1,2,2), which is 4 terms.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000
• Rémy Sigrist, C program

Crossrefs

Cf. A331614, A358537. a(1-16) in A138099 are the same.

Programs

C

See Links section.