A213729 Sequence A179016 reduced modulo 2.

0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1

Offset

0

Comments

It holds for all n>=1 that a(n) = A179016(n)-A213723(A179016(n-1)) meaning that a(n) = 1 when the next node upwards in the infinite trunk of beanstalk sequence (A179016) is the larger of the two possible branches from A179016(n), and 0 when it is the smaller of the said branches. That is, this sequence tells whether A179016 proceeds "left" or "right" at each step.

If we were able to find the values of this sequence "a priori" (without needing the value of A179016 at the same point and taking modulo 2 from it), then A179016 could be computed in a more straightforward "bottom-up manner", as then we would have enough information to find the correct path in the binary tree of beanstalk up to the infinity.

Links

Antti Karttunen, Table of n, a(n) for n = 0..2493

Formula

a(n) = A000035(A179016(n)).

Prog

(Scheme): (define (A213729 n) (A000035 (A179016 n)))
;; Alternative definition:
(define (A213729v2 n) (if (zero? n) n (- (A179016 n) (A213723 (A179016 (-1+ n))))))

Crossrefs

a(n) = A000035(A179016(n)). Binary complement of A213728. Cf. A213730, A213733. Run lengths: A218545.

Sequence in context: A066829 A194664 A285975 * A296135 A174207 A048820

Adjacent sequences: A213726 A213727 A213728 * A213730 A213731 A213732

Keyword

nonn

Author

Antti Karttunen, Nov 01 2012

Extensions

Offset changed from 1 to 0 by Antti Karttunen, Nov 05 2012

Status

approved