A366548 -id:A366548 - cp's OEIS frontend

A366549 a(0) = 0; for n > 0, a(n) is the number of terms prior to and including the term a(n-1-a(n-1)) that equal a(n-1-a(n-1)).

0, 1, 1, 1, 2, 2, 3, 3, 1, 2, 2, 4, 2, 4, 3, 1, 3, 2, 5, 2, 6, 3, 1, 5, 1, 2, 2, 7, 1, 1, 8, 6, 8, 7, 9, 8, 1, 3, 1, 6, 2, 11, 1, 1, 12, 2, 13, 2, 11, 6, 13, 6, 11, 1, 3, 5, 2, 7, 2, 13, 1, 3, 14, 2, 8, 13, 3, 15, 3, 4, 4, 9, 1, 2, 2, 16, 3, 16, 8, 4, 1, 5, 11, 2, 4, 17, 10, 11, 11, 2, 5, 1, 5

Offset: 0

Scott R. Shannon, Oct 13 2023

In the first 10 million terms the value 1 appears the most often, 13584 times, although the count of neighboring values is less than 2% different. It is unknown if this stays the most common term as n increases. In the same range on fifty occasions there are three consecutive equal terms, the second time, after the three 1's at the start of the sequence, being a(406) = a(407) = a(408) = 11. It is unknown if four or more consecutive terms eventually appear.

			a(2) = 1 as a(2-1-a(2-1)) = a(1-1) = a(0) = 0, and there is one term prior to or equal to a(0) that equals 0, namely a(0).
a(6) = 3 as a(6-1-a(6-1)) = a(5-2) = a(3) = 1, and there are three terms prior to or equal to a(3) that equal 1, namely a(1), a(2) and a(3).

Scott R. Shannon, Table of n, a(n) for n = 0..10000
Scott R. Shannon, Image of the first 10 million terms.

Cf. A366548, A363193, A354971, A181391, A342585.

cp's OEIS Frontend

A366549 a(0) = 0; for n > 0, a(n) is the number of terms prior to and including the term a(n-1-a(n-1)) that equal a(n-1-a(n-1)).

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