A289322 Number of 1s in the first 2^n entries of the Kolakoski sequence, A000002.

1, 1, 2, 4, 8, 17, 32, 64, 129, 256, 513, 1024, 2051, 4093, 8192, 16381, 32746, 65523, 131082, 262168, 524262, 1048547, 2097100, 4194345, 8388733, 16777351, 33554669, 67109796, 134219275, 268437750, 536872179

Offset

0,3

Links

Richard P. Brent, Table of n, a(n) for n = 0..64

Richard P. Brent and Judy-anne H. Osborn, A fast algorithm for the Kolakoski sequence, Dec. 2016

J. Nilsson, A Space Efficient Algorithm for the Calculation of the Digit Distribution in the Kolakoski Sequence, arXiv preprint arXiv:1110.4228 [math.CO], 2011.

M. Rao, Trucs et bidules sur la séquence de Kolakoski, Oct. 2012.

Formula

a(n) = (2^n + A088568(2^n))/2 = (2^n - A289323(n))/2.

Example

The first 32 entries of the Kolakoski sequence, A000002, are 12211212212211211221211212211211. From this we see that a(5)=17, since among the first 2^5 letters, 17 of them are 1s.

Crossrefs

Cf. A000002. Analogous for powers of ten is A195206. Equivalent but with smaller entries is A289323. Closely related are A054353, A074286, A088568, A156077.

Sequence in context: A080281 A172446 A320331 * A349842 A049962 A056184

Adjacent sequences: A289319 A289320 A289321 * A289323 A289324 A289325

Keyword

nonn

Author

Richard P. Brent, Jul 05 2017

Status

approved