A244226 Length of runs in A244221 (Greedy Catalan Base, A014418, reduced modulo 2).

1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 2

Offset

0,5

Comments

Also the length of runs in A244220.

Note: The indexing of A244220 and A244221 starts from zero, so the starting offset of this sequence is zero also.

Links

Antti Karttunen, Table of n, a(n) for n = 0..4120

Example

The first time we obtain value three at a(112) = 3, indicating that the first run of 3 in A244220 and A244221 starts at the position A244219(112) = 130, and indeed, it's the first time there are three consecutive "even" representations in Greedy Catalan Base:
A014418(130) = 30020,
A014418(131) = 30100,
A014418(132) = 100000,
A014418(133) = 100001.

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(definec (A244226 n) (if (zero? n) 1 (let* ((prev_run_ends_at (A244218 (- n 1))) (prevpar (A244221 prev_run_ends_at))) (let loop ((i (+ 1 prev_run_ends_at))) (cond ((= (A244221 (+ i 1)) prevpar) (- i prev_run_ends_at)) (else (loop (+ i 1))))))))

Crossrefs

A244218 gives the partial sums (the ending points of corresponding runs), while A244219 gives the starting points.

A244227 gives the even bisection, while the odd bisection is A000012 (all-1 sequence).

Sequence in context: A120888 A031230 A355032 * A344590 A111616 A299152

Adjacent sequences: A244223 A244224 A244225 * A244227 A244228 A244229

Keyword

nonn

Author

Antti Karttunen, Jun 23 2014

Status

approved