A374998 Position of the last requested element when the elements of the n-th composition (in standard order) are requested from a self-organizing list initialized to (1, 2, 3, ...), using the transpose updating strategy.

1, 2, 1, 3, 2, 2, 1, 4, 1, 1, 1, 3, 2, 2, 1, 5, 1, 3, 1, 3, 2, 2, 1, 4, 1, 1, 1, 3, 2, 2, 1, 6, 1, 2, 1, 2, 1, 3, 1, 4, 3, 1, 1, 3, 2, 2, 1, 5, 1, 3, 1, 3, 2, 2, 1, 4, 1, 1, 1, 3, 2, 2, 1, 7, 1, 2, 1, 4, 2, 2, 1, 4, 2, 2, 1, 2, 1, 3, 1, 5, 2, 1, 2, 3, 2, 2, 1

Offset: 1

Author

Pontus von Brömssen, Jul 27 2024

Keywords

• nonn

Comments

See A374993 for details.

Crossrefs

Row n=1 of A375001.

Analogous sequences for other updating strategies: A374997, A374999, A375000.

Cf. A025480, A066099 (compositions in standard order), A333766, A374993.

Formula

a(n) = A374993(n) - A374993(A025480(n-1)).

Sum_{j=1..m} a(n*2^j+2^(j-1)) = m*(m+1)/2 if m >= A333766(n). This is a consequence of the fact that the first m positions of the list are occupied by the elements 1, ..., m, as long as no element larger than m has been requested so far.