A244226 - OEIS

%I #12 Jun 25 2014 13:12:40

%S 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,

%T 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,

%U 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

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

%C Also the length of runs in A244220.

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

%H Antti Karttunen, <a href="/A244226/b244226.txt">Table of n, a(n) for n = 0..4120</a>

%e 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:

%e A014418(130) = 30020,

%e A014418(131) = 30100,

%e A014418(132) = 100000,

%e A014418(133) = 100001.

%o (Scheme, with _Antti Karttunen_'s IntSeq-library)

%o (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))))))))

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

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

%K nonn

%O 0,5

%A _Antti Karttunen_, Jun 23 2014