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

1,2

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.

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

Example

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)

Prog

(PARI) See Links section.

Crossrefs

Cf. A000045, A001177, A309200.

Sequence in context: A193798 A101409 A271862 * A131401 A061446 A280690

Adjacent sequences: A309370 A309371 A309372 * A309374 A309375 A309376

Keyword

nonn

Author

Rémy Sigrist, Jul 26 2019

Status

approved