A279205 - OEIS

%I #16 Aug 20 2021 13:38:43

%S 0,0,0,1,0,1,1,1,2,1,2,1,1,2,1,1,2,3,4,1,3,2,1,6,1,2,1,4,7,5,2,3,1,4,

%T 2,1,1,5,2,1,3,1,1,3,3,3,3,8,2,1,2,2,1,3,2,2,1,1,1,1,3,2,1,1,2,1,4,1,

%U 2,4,1,2,3,1,1,1,2,1,1,5,1,1,1,5,4,3,2,2,2,1,1,1,1,1,1,3,2,2,1,1

%N Length of second run of 1's in binary representation of Catalan(n).

%C Suggested by A279026.

%C What combinatorial problem is this the answer to?

%H Chai Wah Wu, <a href="/A279205/b279205.txt">Table of n, a(n) for n = 0..10000</a>

%e A000108(13) = 742900_10 = A264663(13) = 10110101010111110100_2, so a(13) = 2.

%t Q = {};

%t Num = 100;

%t T = Table[IntegerDigits[CatalanNumber[n], 2], {n, 0, Num}];

%t For[i = 1, i <= Num, i++,

%t c = 0; j = 1;

%t While[T[[i]][[j]] == 1, j++];

%t While[T[[i]][[j]] == 0, j++];

%t c = j;

%t While[T[[i]][[j]] == 1, j++];

%t c = j - c;

%t AppendTo[Q, c]

%t ];

%t Q (* _Benedict W. J. Irwin_, Dec 21 2016 *)

%t Join[{0,0,0,1,0},Length[Split[IntegerDigits[#,2]][[3]]]&/@ CatalanNumber[ Range[5,100]]] (* _Harvey P. Dale_, Aug 20 2021 *)

%Y Cf. A000108, A264663, A279026, A279206.

%K nonn,base

%O 0,9

%A _N. J. A. Sloane_, Dec 21 2016

%E a(19) to a(99) from _Benedict W. J. Irwin_, Dec 21 2016