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

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, 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, 6, 1, 3, 2, 1, 1, 2, 6, 1, 1, 1, 2, 2, 2, 3, 6, 1, 1, 1, 1, 1, 1

Offset: 0

Author

N. J. A. Sloane, Dec 22 2016

Keywords

• nonn
• base
• look

Comments

What combinatorial problem is this the answer to?

Examples

			A000108(13) = 742900_10 = A264663(13) = 10110101010111110100_2, so a(13) = 1.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000108, A264663, A279026, A279205.

Programs

Maple

f:= proc(n) local L; uses ListTools;
    L:= [1,op(convert(binomial(2*n,n)/(n+1),base,2))];
    L:= Reverse(L[2..-1]-L[1..-2]);
    Search(-1,L) - Search(1,L);
end proc:
map(f, [$0..100]); # Robert Israel, Dec 22 2016

Mathematica

Table[First[Map[Length, DeleteCases[Split@ IntegerDigits[CatalanNumber@ n, 2], w_ /; Times @@ w > 0]] /. {} -> {0}], {n, 0, 89}] (* Michael De Vlieger, Dec 22 2016 *)