cp's OEIS Frontend

A279026 Size of blocks of 1's in the second column of Catalan numbers written in binary and left-aligned.

%I A279026 #26 Dec 22 2016 22:12:25
%S A279026 1,1,2,4,6,10,15,23,36,59,93,148,234,372,592,939,1490,2366,3754,5959,
%T A279026 9460,15017,23838,37841,60068,95352,151362
%N A279026 Size of blocks of 1's in the second column of Catalan numbers written in binary and left-aligned.
%C A279026 What combinatorial problem is this the answer to? - _N. J. A. Sloane_, Dec 21 2016
%C A279026 Appears to be strictly increasing for n > 1. - _Chai Wah Wu_, Dec 22 2016
%e A279026 Left-align the binary representation of the Catalan numbers:
%e A279026 1
%e A279026 1
%e A279026 10
%e A279026 101
%e A279026 1110
%e A279026 101010
%e A279026 10000100
%e A279026 110101101
%e A279026 10110010110
%e A279026 The first column is all 1's, by definition.
%e A279026 The next column appears to have blocks of 1's and 0's.
%e A279026 The sizes of the blocks make this sequence.
%e A279026 The values of this column may be generated with the MMA code:
%e A279026 Table[If[2^Floor[Log2[CatalanNumber[n]]] + 2^(Floor[Log2[CatalanNumber[n]]] - 1) < CatalanNumber[n], 1, 0], {n, 1, 1000}].
%t A279026 Num = 10000;
%t A279026 T = Table[If[2^Floor[Log2[CatalanNumber[n]]] +2^(Floor[Log2[CatalanNumber[n]]] - 1) < CatalanNumber[n], 1, 0], {n, 1, Num}]; S = {};
%t A279026 For[i = 1, i < Num, i++, j = 0; If[T[[i]] == 1, While[T[[i]] == 1, i++; j++]; AppendTo[S, j];];]; S
%Y A279026 Cf. A000108.
%K A279026 nonn,base
%O A279026 1,3
%A A279026 _Benedict W. J. Irwin_, Dec 12 2016
%E A279026 a(21)-a(27) from _Chai Wah Wu_, Dec 22 2016