A265405 Start with a(1) = 1, then always choose for a(n) the least unused number such that A193231(a(n)*a(n-1)) = A193231(a(n)) * A193231(a(n-1)), where A193231 is an involution of natural numbers called Blue code.

1, 2, 3, 4, 5, 6, 16, 7, 17, 8, 15, 32, 12, 10, 18, 20, 19, 256, 9, 14, 34, 48, 40, 50, 33, 60, 257, 11, 97, 258, 13, 101, 209, 65536, 21, 259, 64, 30, 65, 51, 80, 24, 84, 36, 85, 66, 260, 22, 4352, 26, 4368, 28, 4369, 37, 768, 41, 770, 42, 771, 68, 90, 272, 45, 273, 56, 1200, 952, 4096, 23, 4097, 27, 4098, 86, 512, 54

Offset

1,2

Comments

Does this sequence die after a(144) = 46 ?

No, a(145) = 16777216, but whether the sequence is finished remains open. - Rémy Sigrist, Feb 15 2019

The next unused number of the form 2^2^k is always a valid choice, so this sequence is infinite. - Charlie Neder, Apr 14 2019

Links

Rémy Sigrist, Table of n, a(n) for n = 1..183 (first 144 terms from Antti Karttunen) [More terms needed for b-file.]

Rémy Sigrist, PARI program for A265405

Prog

(Scheme, with defineperm1-macro from Antti Karttunen's IntSeq-library)
(defineperm1 (A265405 n) (cond ((= 1 n) n) (else (let ((prev (A265405 (- n 1)))) (let loop ((k 1)) (cond ((and (not-lte? (A265406 k) (- n 1)) (= (A193231 (* k prev)) (* (A193231 k) (A193231 prev)))) k) (else (loop (+ 1 k)))))))))
;; We consider a > b (i.e. not less than b) also in case a is #f.
;; (Because of the stateful caching system used by defineperm1-macro):
(define (not-lte? a b) (cond ((not (number? a)) #t) (else (> a b))))
(PARI) See Links section.

Crossrefs

Inverse: A265406.

Cf. A193231.

Cf. A266195, A266351, A266405 (sequences with similar definitions, of which at least the first two are known to be infinite and also bijective).

Sequence in context: A039061 A138987 A318534 * A171610 A004835 A037341

Adjacent sequences: A265402 A265403 A265404 * A265406 A265407 A265408

Keyword

nonn,base

Author

Antti Karttunen, Dec 29 2015

Status

approved