A374997 - OEIS

A374997

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 move-to-front 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, 2, 2, 1, 6, 2, 3, 1, 1, 3, 3, 1, 4, 3, 1, 1, 3, 2, 2, 1, 5, 2, 3, 1, 3, 2, 2, 1, 4, 2, 1, 1, 3, 2, 2, 1, 7, 2, 3, 1, 4, 3, 3, 1, 4, 2, 1, 1, 2, 2, 3, 1, 5, 3, 2, 1, 3, 2, 2, 1

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

See A374992 for details.

LINKS

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

FORMULA

a(n) = A374992(n) - A374992(A025480(n-1)).

a(n) = A375001(k,n) whenever k >= A333766(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: A374998, A374999, A375000, A375001.

Cf. A025480, A066099 (compositions in standard order), A333766, A374992.

Sequence in context: A260088 A364969 A374999 * A339399 A272911 A371014

Adjacent sequences: A374994 A374995 A374996 * A374998 A374999 A375000

KEYWORD

nonn

AUTHOR

Pontus von Brömssen, Jul 27 2024

STATUS

approved