A255567 a(1) = 1, a(2) = 2, after which, a(2n+1) = 1 + a(2n), a(2n) = A255411(a(n)).

1, 2, 3, 12, 13, 16, 17, 72, 73, 76, 77, 90, 91, 94, 95, 480, 481, 484, 485, 498, 499, 502, 503, 576, 577, 580, 581, 594, 595, 598, 599, 3600, 3601, 3604, 3605, 3618, 3619, 3622, 3623, 3696, 3697, 3700, 3701, 3714, 3715, 3718, 3719, 4200, 4201, 4204, 4205, 4218, 4219, 4222, 4223, 4296, 4297, 4300, 4301, 4314, 4315, 4318, 4319

Offset

1,2

Comments

From 2 onward, the sequence seems to give those n for which A256450(A255411(n))+1 = A255411(A256450(n)), i.e., grandparents for those cousins in tree A255566 where the cousin at the right side is one more than the cousin at the left side.

Links

Antti Karttunen, Table of n, a(n) for n = 1..1023

Formula

a(1) = 1, a(2) = 2, after which, a(2n+1) = 1 + a(2n), a(2n) = A255411(a(n)).

Example

This sequence can be represented as a binary tree. Apart from the 1 at root, and its children 2 and 3, from then on each left hand child is produced as A255411(n), and each right hand child as 1 + A255411(n) when parent contains n >= 2:
                   ..................1..................
                  2                                     3
        12......./ \.......13                 16......./ \.......17
       / \                 / \               / \                 / \
      /   \               /   \             /   \               /   \
     /     \             /     \           /     \             /     \
   72       73         76       77       90       91         94       95
480  481 484  485   498  499 502  503 576  577 580  581   594  595 598  599
etc.

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(definec (A255567 n) (cond ((<= n 2) n) ((odd? n) (+ 1 (A255567 (- n 1)))) (else (A255411 (A255567 (/ n 2))))))
;; This for now conjectured to be equal from a(2) onward:
(define A255567 (MATCHING-POS 2 1 (lambda (n) (= (+ 1 (A256450 (A255411 n))) (A255411 (A256450 n))))))

Crossrefs

Cf. A256450, A255411. See also the tree illustration in A255566.

Sequence in context: A302843 A037321 A227745 * A039565 A032805 A239017

Adjacent sequences: A255564 A255565 A255566 * A255568 A255569 A255570

Keyword

nonn

Author

Antti Karttunen, May 05 2015

Extensions

Edited because of the changed starting offset of A256450 - Antti Karttunen, May 30 2016

Status

approved