

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



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

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


KEYWORD

nonn,base


AUTHOR



STATUS

approved



