A236859 The length of the initial ascent 123... in the n-th Catalan numeral, A239903(n).

0, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 2, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2

Offset

0,5

Links

Antti Karttunen, Table of n, a(n) for n = 0..16796

Formula

a(0) = 0, and for n>=1, a(n) = A126307(A081291(n))-1.

Each n occurs for the first time (as a record) at the position (C_{n+1})-1, so we have a(A001453(n+1)) = n for all n.

Example

A239903(1) = 1, thus a(1) = 1.
A239903(2) = 10, thus a(2) = 1.
A239903(4) = 12, thus a(4) = 2.
A239903(39) = 1232, thus a(39) = 3.
A239903(58784) = 1234567899, thus a(58784) = 9.
Note that although the range of validity of A239903 is inherently limited by the decimal representation employed, it doesn't matter here: We have a(58785) = 10, as the corresponding 58785th Catalan String is [1,2,3,4,5,6,7,8,9,10], even though A239903 cannot represent that unambiguously.

Prog

(Scheme) (define (A236859 n) (if (zero? n) n (- (A126307 (A081291 n)) 1)))

Crossrefs

Cf. A239903, A236855, A081291, A126307.

Sequence in context: A176505 A338521 A036225 * A278401 A069935 A283530

Adjacent sequences: A236856 A236857 A236858 * A236860 A236861 A236862

Keyword

nonn

Author

Antti Karttunen, Apr 18 2014

Status

approved