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A269363
Lexicographically first injection of natural numbers beginning with a(1)=3 such that for all n >= 1, a(n)*a(n+1) is a fibbinary number (A003714), i.e., has no adjacent 1's in its base-2 representation.
7
3, 6, 7, 12, 11, 15, 22, 24, 14, 19, 27, 38, 28, 23, 46, 48, 43, 30, 39, 35, 59, 44, 31, 75, 62, 87, 51, 83, 56, 47, 88, 54, 76, 55, 96, 86, 60, 71, 67, 70, 78, 112, 79, 107, 102, 91, 120, 139, 118, 140, 119, 142, 131, 134, 155, 240, 156, 135, 152, 108, 95, 92, 103, 179, 184, 115, 147, 224, 94, 175, 123, 150, 111, 158, 214, 163, 203
OFFSET
1,1
COMMENTS
The sequence is conjectured to be a permutation of A091067.
The scatter plot is quite interesting (essentially the same as A269367). Compare also to the graph of A269361.
LINKS
MATHEMATICA
fibbinaryQ[n_] := BitAnd[n, 2 n]==0; a[1]=3; a[n_] := a[n] = For[k=1, True, k++, If[Mod[k, 4] != 1, If[fibbinaryQ[a[n-1] k], If[FreeQ[Array[a, n-1], k], Return[k]]]]]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Mar 02 2016 *)
PROG
(Scheme, with defineperm1-macro from Antti Karttunen's IntSeq-library)
(defineperm1 (A269363 n) (cond ((= 1 n) 3) (else (let ((prev (A269363 (- n 1)))) (let loop ((k 1)) (cond ((and (not-lte? (A269363inv_cache k) (- n 1)) (isa003714? (* k prev))) k) (else (loop (+ 1 k)))))))))
(define (A269363inv_cache n) (A269363 (- n)))
;; 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))))
(define (isA003714? n) (= (* 3 n) (A003987bi n (* 2 n)))) ;; Where A003987bi implements bitwise-XOR (see A003987).
CROSSREFS
Cf. A269367 (the terms ranked with A255070).
Sequence in context: A181683 A084125 A053478 * A138037 A209246 A073934
KEYWORD
nonn,base,look
AUTHOR
Antti Karttunen, Feb 25 2016
STATUS
approved