cp's OEIS Frontend

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.

%I A265405 #21 Apr 15 2019 01:55:55
%S A265405 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,
%T A265405 60,257,11,97,258,13,101,209,65536,21,259,64,30,65,51,80,24,84,36,85,
%U A265405 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
%N 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.
%C A265405 Does this sequence die after a(144) = 46 ?
%C A265405 No, a(145) = 16777216, but whether the sequence is finished remains open. - _Rémy Sigrist_, Feb 15 2019
%C A265405 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
%H A265405 Rémy Sigrist, <a href="/A265405/b265405.txt">Table of n, a(n) for n = 1..183</a> (first 144 terms from Antti Karttunen) [More terms needed for b-file.]
%H A265405 Rémy Sigrist, <a href="/A265405/a265405.gp.txt">PARI program for A265405</a>
%o A265405 (Scheme, with defineperm1-macro from Antti Karttunen's IntSeq-library)
%o A265405 (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)))))))))
%o A265405 ;; We consider a > b (i.e. not less than b) also in case a is #f.
%o A265405 ;; (Because of the stateful caching system used by defineperm1-macro):
%o A265405 (define (not-lte? a b) (cond ((not (number? a)) #t) (else (> a b))))
%o A265405 (PARI) See Links section.
%Y A265405 Inverse: A265406.
%Y A265405 Cf. A193231.
%Y A265405 Cf. A266195, A266351, A266405 (sequences with similar definitions, of which at least the first two are known to be infinite and also bijective).
%K A265405 nonn,base
%O A265405 1,2
%A A265405 _Antti Karttunen_, Dec 29 2015