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A279206 Length of first run of 0's in binary representation of Catalan(n).

%I A279206 #14 Dec 22 2016 22:17:46
%S A279206 0,0,1,1,1,1,4,1,1,2,5,2,2,1,1,2,4,1,3,1,4,1,1,2,2,3,4,2,1,3,1,2,3,1,
%T A279206 1,1,1,2,2,2,3,3,4,3,1,1,2,8,1,1,2,3,5,1,1,1,1,1,1,1,2,2,2,2,3,3,4,4,
%U A279206 6,1,3,2,1,1,2,6,1,1,1,2,2,2,3,6,1,1,1,1,1,1
%N A279206 Length of first run of 0's in binary representation of Catalan(n).
%C A279206 What combinatorial problem is this the answer to?
%H A279206 Robert Israel, <a href="/A279206/b279206.txt">Table of n, a(n) for n = 0..10000</a>
%e A279206 A000108(13) = 742900_10 = A264663(13) = 10110101010111110100_2, so a(13) = 1.
%p A279206 f:= proc(n) local L; uses ListTools;
%p A279206     L:= [1,op(convert(binomial(2*n,n)/(n+1),base,2))];
%p A279206     L:= Reverse(L[2..-1]-L[1..-2]);
%p A279206     Search(-1,L) - Search(1,L);
%p A279206 end proc:
%p A279206 map(f, [$0..100]); # _Robert Israel_, Dec 22 2016
%t A279206 Table[First[Map[Length, DeleteCases[Split@ IntegerDigits[CatalanNumber@ n, 2], w_ /; Times @@ w > 0]] /. {} -> {0}], {n, 0, 89}] (* _Michael De Vlieger_, Dec 22 2016 *)
%Y A279206 Cf. A000108, A264663, A279026, A279205.
%K A279206 nonn,base,look
%O A279206 0,7
%A A279206 _N. J. A. Sloane_, Dec 22 2016