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

0,7

Comments

What combinatorial problem is this the answer to?

Links

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

Example

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

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 *)

Crossrefs

Cf. A000108, A264663, A279026, A279205.

Sequence in context: A096103 A204456 A143441 * A333989 A016527 A010325

Adjacent sequences: A279203 A279204 A279205 * A279207 A279208 A279209

Keyword

nonn,base,look

Author

N. J. A. Sloane, Dec 22 2016

Status

approved