A375000 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, ...), where a requested element at position i is moved to position floor((i+1)/2).

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

Offset: 1

Author

Pontus von Brömssen, Jul 27 2024

Keywords

• nonn

Comments

See A374995 for details.

Crossrefs

Analogous sequences for other updating strategies: A374997, A374998, A374999.

Cf. A025480, A066099 (compositions in standard order), A333766, A374995.

Formula

a(n) = A374995(n) - A374995(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.