This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A244226 #12 Jun 25 2014 13:12:40 %S A244226 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 A244226 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 A244226 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 A244226 Length of runs in A244221 (Greedy Catalan Base, A014418, reduced modulo 2). %C A244226 Also the length of runs in A244220. %C A244226 Note: The indexing of A244220 and A244221 starts from zero, so the starting offset of this sequence is zero also. %H A244226 Antti Karttunen, <a href="/A244226/b244226.txt">Table of n, a(n) for n = 0..4120</a> %e A244226 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 A244226 A014418(130) = 30020, %e A244226 A014418(131) = 30100, %e A244226 A014418(132) = 100000, %e A244226 A014418(133) = 100001. %o A244226 (Scheme, with _Antti Karttunen_'s IntSeq-library) %o A244226 (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 A244226 A244218 gives the partial sums (the ending points of corresponding runs), while A244219 gives the starting points. %Y A244226 A244227 gives the even bisection, while the odd bisection is A000012 (all-1 sequence). %K A244226 nonn %O A244226 0,5 %A A244226 _Antti Karttunen_, Jun 23 2014