

A279026


Size of blocks of 1's in the second column of Catalan numbers written in binary and leftaligned.


2



1, 1, 2, 4, 6, 10, 15, 23, 36, 59, 93, 148, 234, 372, 592, 939, 1490, 2366, 3754, 5959, 9460, 15017, 23838, 37841, 60068, 95352, 151362
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OFFSET

1,3


COMMENTS

What combinatorial problem is this the answer to?  N. J. A. Sloane, Dec 21 2016
Appears to be strictly increasing for n > 1.  Chai Wah Wu, Dec 22 2016


LINKS



EXAMPLE

Leftalign the binary representation of the Catalan numbers:
1
1
10
101
1110
101010
10000100
110101101
10110010110
The first column is all 1's, by definition.
The next column appears to have blocks of 1's and 0's.
The sizes of the blocks make this sequence.
The values of this column may be generated with the MMA code:
Table[If[2^Floor[Log2[CatalanNumber[n]]] + 2^(Floor[Log2[CatalanNumber[n]]]  1) < CatalanNumber[n], 1, 0], {n, 1, 1000}].


MATHEMATICA

Num = 10000;
T = Table[If[2^Floor[Log2[CatalanNumber[n]]] +2^(Floor[Log2[CatalanNumber[n]]]  1) < CatalanNumber[n], 1, 0], {n, 1, Num}]; S = {};
For[i = 1, i < Num, i++, j = 0; If[T[[i]] == 1, While[T[[i]] == 1, i++; j++]; AppendTo[S, j]; ]; ]; S


CROSSREFS



KEYWORD

nonn,base


AUTHOR



EXTENSIONS



STATUS

approved



