The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A279026 Size of blocks of 1's in the second column of Catalan numbers written in binary and left-aligned. 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 (list; graph; refs; listen; history; text; internal format)
 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 Table of n, a(n) for n=1..27. EXAMPLE Left-align 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 Cf. A000108. Sequence in context: A309173 A116084 A108925 * A120549 A167270 A355108 Adjacent sequences: A279023 A279024 A279025 * A279027 A279028 A279029 KEYWORD nonn,base AUTHOR Benedict W. J. Irwin, Dec 12 2016 EXTENSIONS a(21)-a(27) from Chai Wah Wu, Dec 22 2016 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 12 11:23 EDT 2024. Contains 375850 sequences. (Running on oeis4.)