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A309373 a(n) is the smallest divisor of F(n+1) not already in the sequence (where F denotes the Fibonacci numbers A000045).

%I A309373 #10 Jul 26 2019 16:25:36
%S A309373 1,2,3,5,4,13,7,17,11,89,6,233,29,10,21,1597,8,37,15,26,199,28657,9,
%T A309373 25,521,34,39,514229,20,557,47,178,3571,65,12,73,113,466,33,2789,52,
%U A309373 433494437,43,61,139,2971215073,14,97,55,3194,699,953,19,445,49,74,59
%N A309373 a(n) is the smallest divisor of F(n+1) not already in the sequence (where F denotes the Fibonacci numbers A000045).
%C A309373 This sequence is the Fibonacci variant of A309200.
%C A309373 This sequence is a permutation of the natural numbers as for any m > 0, there are infinitely many multiples of m in A000045.
%H A309373 Daniel Suteu, <a href="/A309373/b309373.txt">Table of n, a(n) for n = 1..1258</a>
%H A309373 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%H A309373 Rémy Sigrist, <a href="/A309373/a309373.gp.txt">PARI program for A309373</a>
%e A309373 The first terms, alongside the divisors of F(n+1), are:
%e A309373   n   a(n)  div(F(n+1))
%e A309373   --  ----  ----------------------------------------
%e A309373    1     1  (1)
%e A309373    2     2  (1, 2)
%e A309373    3     3  (1, 3)
%e A309373    4     5  (1, 5)
%e A309373    5     4  (1, 2, 4, 8)
%e A309373    6    13  (1, 13)
%e A309373    7     7  (1, 3, 7, 21)
%e A309373    8    17  (1, 2, 17, 34)
%e A309373    9    11  (1, 5, 11, 55)
%e A309373   10    89  (1, 89)
%e A309373   11     6  (1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144)
%e A309373   12   233  (1, 233)
%o A309373 (PARI) See Links section.
%Y A309373 Cf. A000045, A001177, A309200.
%K A309373 nonn
%O A309373 1,2
%A A309373 _Rémy Sigrist_, Jul 26 2019