A236859 - OEIS

%I #19 May 09 2014 23:14:09

%S 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,

%T 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,

%U 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2

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

%H Antti Karttunen, <a href="/A236859/b236859.txt">Table of n, a(n) for n = 0..16796</a>

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

%F 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.

%e A239903(1) = 1, thus a(1) = 1.

%e A239903(2) = 10, thus a(2) = 1.

%e A239903(4) = 12, thus a(4) = 2.

%e A239903(39) = 1232, thus a(39) = 3.

%e A239903(58784) = 1234567899, thus a(58784) = 9.

%e 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.

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

%Y Cf. A239903, A236855, A081291, A126307.

%K nonn

%O 0,5

%A _Antti Karttunen_, Apr 18 2014