cp's OEIS Frontend

A279205 Length of second run of 1's in binary representation of Catalan(n).

%I A279205 #16 Aug 20 2021 13:38:43
%S A279205 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 A279205 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 A279205 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 A279205 Length of second run of 1's in binary representation of Catalan(n).
%C A279205 Suggested by A279026.
%C A279205 What combinatorial problem is this the answer to?
%H A279205 Chai Wah Wu, <a href="/A279205/b279205.txt">Table of n, a(n) for n = 0..10000</a>
%e A279205 A000108(13) = 742900_10 = A264663(13) = 10110101010111110100_2, so a(13) = 2.
%t A279205 Q = {};
%t A279205 Num = 100;
%t A279205 T = Table[IntegerDigits[CatalanNumber[n], 2], {n, 0, Num}];
%t A279205 For[i = 1, i <= Num, i++,
%t A279205 c = 0; j = 1;
%t A279205 While[T[[i]][[j]] == 1, j++];
%t A279205 While[T[[i]][[j]] == 0, j++];
%t A279205 c = j;
%t A279205 While[T[[i]][[j]] == 1, j++];
%t A279205 c = j - c;
%t A279205 AppendTo[Q, c]
%t A279205 ];
%t A279205 Q (* _Benedict W. J. Irwin_, Dec 21 2016 *)
%t A279205 Join[{0,0,0,1,0},Length[Split[IntegerDigits[#,2]][[3]]]&/@ CatalanNumber[ Range[5,100]]] (* _Harvey P. Dale_, Aug 20 2021 *)
%Y A279205 Cf. A000108, A264663, A279026, A279206.
%K A279205 nonn,base
%O A279205 0,9
%A A279205 _N. J. A. Sloane_, Dec 21 2016
%E A279205 a(19) to a(99) from _Benedict W. J. Irwin_, Dec 21 2016