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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. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 26 20:24 EDT 2019. Contains 324380 sequences. (Running on oeis4.)