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%I #7 Jul 22 2017 08:32:36
%S 0,1,1,2,1,1,2,2,3,1,1,1,1,1,2,2,2,2,2,3,3,3,4,1,1,1,1,1,1,1,1,1,1,1,
%T 1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,5,1,1,1,
%U 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
%N a(n) is the length of the leftmost ascent (i.e., height of the first peak) in the n-th Dyck path encoded by A014486(n).
%C In other words, this sequence gives the number of leading 1's in the terms of A063171.
%F a(n) = A090996(A014486(n)).
%e A014486(20) = 228 (11100100 in binary), encodes the following Dyck path:
%e /\
%e / \/\
%e / \
%e and the first rising (left-hand side) slope has length 3, thus a(20)=3.
%Y a(n) = A099563(A071156(n)) = A057515(A125985(n)) = A080237(A057164(n)) = A057515(A057504(A057164(n))).
%K nonn
%O 0,4
%A _Antti Karttunen_, Jan 02 2007
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