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A289322 Number of 1s in the first 2^n entries of the Kolakoski sequence, A000002. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
Richard P. Brent and Judy-anne H. Osborn, A fast algorithm for the Kolakoski sequence, Dec. 2016
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
KEYWORD
nonn
AUTHOR
Richard P. Brent, Jul 05 2017
STATUS
approved

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Last modified June 19 22:07 EDT 2024. Contains 373507 sequences. (Running on oeis4.)