A366574 a(1) = 1; for n > 1, a(n) is the maximum positive k such that all terms a(t), a(t-m), a(t-2*m), ..., a(t-(k-1)*m), for 0<t<n and any m>=1, are equal.

1, 1, 2, 1, 2, 2, 2, 3, 1, 2, 3, 2, 3, 2, 3, 3, 3, 4, 1, 2, 3, 4, 2, 3, 4, 2, 3, 4, 3, 4, 3, 4, 3, 4, 4, 4, 5, 1, 2, 3, 4, 5, 2, 3, 4, 5, 2, 3, 4, 5, 3, 4, 5, 3, 4, 5, 3, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 5, 5, 6, 1, 2, 3, 4, 5, 6, 2, 3, 4, 5, 6, 2, 3, 4, 5, 6, 3, 4, 5, 6, 3, 4, 5, 6, 3, 4, 5, 6, 4

Offset

1,3

Comments

The terms form quickly form a repetitive pattern of arithmetic progressions of increasing length, see the graph. This leads to any given value t eventually being in a progression of length t+1 which then never increases.

See A366724 for the index where a number first appears.

Links

Scott R. Shannon, Table of n, a(n) for n = 1..10000

Example

a(3) = 2 as a(2) = 1 and a(2) = a(1) = 1.
a(11) = 3 as a(10) = 2 and a(7) = a(6) = a(5) = 2.
a(18) = 4 as a(17) = 3 and a(17) = a(15) = a(13) = a(11) = 3.

Crossrefs

Cf. A366724, A178976, A308638, A229037.

Sequence in context: A067995 A135551 A065531 * A256558 A239281 A024936

Adjacent sequences: A366571 A366572 A366573 * A366575 A366576 A366577

Keyword

nonn

Author

Scott R. Shannon, Oct 13 2023

Status

approved