

A265405


Start with a(1) = 1, then always choose for a(n) the least unused number such that A193231(a(n)*a(n1)) = A193231(a(n)) * A193231(a(n1)), 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
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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 bfile.]
Rémy Sigrist, PARI program for A265405


PROG

(Scheme, with defineperm1macro from Antti Karttunen's IntSeqlibrary)
(defineperm1 (A265405 n) (cond ((= 1 n) n) (else (let ((prev (A265405 ( n 1)))) (let loop ((k 1)) (cond ((and (notlte? (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 defineperm1macro):
(define (notlte? 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



