login
A236859
The length of the initial ascent 123... in the n-th Catalan numeral, A239903(n).
6
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
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Apr 18 2014
STATUS
approved