A380107 a(1) = 0; for n >= 1, if there exists an m < n such that a(m) = a(n), take the largest such m and let a(n+1) be the number of distinct runs in the subsequence a(m)..a(n-1). Otherwise, a(n+1) = 0.

0, 0, 1, 0, 2, 0, 2, 2, 1, 4, 0, 4, 2, 4, 2, 2, 1, 5, 0, 6, 0, 2, 5, 4, 7, 0, 5, 4, 4, 1, 8, 0, 5, 5, 1, 4, 5, 3, 0, 6, 11, 0, 3, 4, 6, 5, 6, 2, 12, 0, 7, 13, 0, 3, 9, 0, 3, 3, 1, 13, 6, 10, 0, 6, 3, 6, 2, 11, 14, 0, 6, 5, 14, 4, 15, 0, 6, 6, 1, 13, 13, 1, 2, 11, 11

Offset

1,5

Comments

This is a variant of Van Eck's sequence A181391 in which we count distinct runs of consecutive equal values rather than individual terms.

The longest run in the sequence has length 2.

Links

Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000

Neal Gersh Tolunsky, Ordinal transform of 100000 terms

Neal Gersh Tolunsky, First differences of 100000 terms

Example

a(10)=4: We find that the most recent occurrence of a(n) = a(9) = 1 is a(3) = 1. In between a(3) and a(8), we find 4 distinct runs: [1]; [0]; [2]; [2,2]. So a(10)=4.

Crossrefs

Cf. A380106, A268755.

Sequence in context: A286222 A029273 A117963 * A321594 A112803 A124242

Adjacent sequences: A380104 A380105 A380106 * A380108 A380109 A380110

Keyword

nonn

Author

Neal Gersh Tolunsky, Jan 12 2025

Status

approved