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

1, 2, 3, 5, 4, 13, 7, 17, 11, 89, 6, 233, 29, 10, 21, 1597, 8, 37, 15, 26, 199, 28657, 9, 25, 521, 34, 39, 514229, 20, 557, 47, 178, 3571, 65, 12, 73, 113, 466, 33, 2789, 52, 433494437, 43, 61, 139, 2971215073, 14, 97, 55, 3194, 699, 953, 19, 445, 49, 74, 59

Offset: 1

Author

Rémy Sigrist, Jul 26 2019

Keywords

• nonn

Comments

This sequence is the Fibonacci variant of A309200.

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

Examples

			The first terms, alongside the divisors of F(n+1), are:
  n   a(n)  div(F(n+1))
  --  ----  ----------------------------------------
   1     1  (1)
   2     2  (1, 2)
   3     3  (1, 3)
   4     5  (1, 5)
   5     4  (1, 2, 4, 8)
   6    13  (1, 13)
   7     7  (1, 3, 7, 21)
   8    17  (1, 2, 17, 34)
   9    11  (1, 5, 11, 55)
  10    89  (1, 89)
  11     6  (1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144)
  12   233  (1, 233)
		

Links

• Daniel Suteu, Table of n, a(n) for n = 1..1258
• Index entries for sequences that are permutations of the natural numbers
• Rémy Sigrist, PARI program for A309373

Crossrefs

Cf. A000045, A001177, A309200.

Programs

PARI

See Links section.