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
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Dec 29 2015
STATUS
approved