%I #10 Jul 26 2019 16:25:36

%S 1,2,3,5,4,13,7,17,11,89,6,233,29,10,21,1597,8,37,15,26,199,28657,9,

%T 25,521,34,39,514229,20,557,47,178,3571,65,12,73,113,466,33,2789,52,

%U 433494437,43,61,139,2971215073,14,97,55,3194,699,953,19,445,49,74,59

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

%C This sequence is the Fibonacci variant of A309200.

%C This sequence is a permutation of the natural numbers as for any m > 0, there are infinitely many multiples of m in A000045.

%H Daniel Suteu, <a href="/A309373/b309373.txt">Table of n, a(n) for n = 1..1258</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%H Rémy Sigrist, <a href="/A309373/a309373.gp.txt">PARI program for A309373</a>

%e The first terms, alongside the divisors of F(n+1), are:

%e n a(n) div(F(n+1))

%e -- ---- ----------------------------------------

%e 1 1 (1)

%e 2 2 (1, 2)

%e 3 3 (1, 3)

%e 4 5 (1, 5)

%e 5 4 (1, 2, 4, 8)

%e 6 13 (1, 13)

%e 7 7 (1, 3, 7, 21)

%e 8 17 (1, 2, 17, 34)

%e 9 11 (1, 5, 11, 55)

%e 10 89 (1, 89)

%e 11 6 (1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144)

%e 12 233 (1, 233)

%o (PARI) See Links section.

%Y Cf. A000045, A001177, A309200.

%K nonn

%O 1,2

%A _Rémy Sigrist_, Jul 26 2019