A374999 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 frequency-count updating strategy.

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

Offset

1,2

Comments

See A374994 for details.

Links

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

Formula

a(n) = A374994(n) - A374994(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

Analogous sequences for other updating strategies: A374997, A374998, A375000.

Cf. A025480, A066099 (compositions in standard order), A333766, A374994.

Sequence in context: A368544 A260088 A364969 * A374997 A339399 A272911

Adjacent sequences: A374996 A374997 A374998 * A375000 A375001 A375002

Keyword

nonn

Author

Pontus von Brömssen, Jul 27 2024

Status

approved