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