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%I #6 Feb 28 2016 07:58:57
%S 1,2,4,5,8,9,16,10,13,20,17,32,18,29,36,33,40,26,21,49,42,52,25,41,50,
%T 82,57,45,53,80,34,64,37,113,74,125,84,61,72,58,73,65,68,69,128,66,
%U 129,132,133,77,114,81,117,90,104,85,98,89,93,100,105,161,106,97,169,122,137,157,138,136,121,141,149,221,153,109,160,116,144
%N Lexicographically first injection of natural numbers beginning with a(1)=1 such that a(n)*a(n+1) is a fibbinary number (A003714), i.e., has no adjacent 1's in its base-2 representation.
%C The sequence is conjectured to be a permutation of A091072.
%H Antti Karttunen, <a href="/A269361/b269361.txt">Table of n, a(n) for n = 1..65537</a>
%o (Scheme, with defineperm1-macro from _Antti Karttunen_'s IntSeq-library)
%o (defineperm1 (A269361 n) (cond ((= 1 n) n) (else (let ((prev (A269361 (- n 1)))) (let loop ((k 1)) (cond ((and (not-lte? (A269361inv_cache k) (- n 1)) (isa003714? (* k prev))) k) (else (loop (+ 1 k)))))))))
%o (define (A269361inv_cache n) (A269361 (- n)))
%o ;; We consider a > b (i.e. not less than b) also in case a is #f.
%o ;; (Because of the stateful caching system used by defineperm1-macro):
%o (define (not-lte? a b) (cond ((not (number? a)) #t) (else (> a b))))
%Y Cf. A003714, A091072, A266121, A266191, A269363, A269365, A269366.
%K nonn,base
%O 1,2
%A _Antti Karttunen_, Feb 25 2016
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