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

1,2

Comments

See A374993 for details.

Links

Table of n, a(n) for n=1..87.

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.

Crossrefs

Row n=1 of A375001.

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

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

Sequence in context: A072339 A342507 A261337 * A375000 A337195 A368544

Adjacent sequences: A374995 A374996 A374997 * A374999 A375000 A375001

Keyword

nonn

Author

Pontus von Brömssen, Jul 27 2024

Status

approved