A102867 Prime differences between k-th prime and k-th Fibonacci number.

-2, -3, -5, 2, 11, 107, 563, 46279, 3524441, 4807526753, 47068900554068939361891195233676009091941689423

Offset

1,1

Comments

Note that for k>3, F(k) - Prime(k) cannot be prime if k is prime.

The next term -- a(11) -- has 110 digits. - Harvey P. Dale, Mar 19 2017

Links

Table of n, a(n) for n=1..11.

Formula

Fibonacci(k) - Prime(k) iff prime. Intersection of {A000045(i) - A000040(i)} and {A000040(j)}. Prime values of A100700.

Example

F(2)-Prime(2) = 1 - 3 = -2.
F(3)-Prime(3) = 2 - 5 = -3.
F(6)-Prime(6) = 8 - 13 = -5.
F(8)-Prime(8) = 21 - 19 = 2.
F(9)-Prime(9) = 34 - 23 = 11.
F(12)-Prime(12) = 144 - 37 = 107.
F(15)-Prime(15) = 610 - 47 = 563.
F(24)-Prime(24) = 46368 - 89 = 46279.
F(33)-Prime(33) = 3524578 - 137 = 3524441.

Mathematica

With[{nn=600}, Select[#[[1]]-#[[2]]&/@Thread[{Fibonacci[Range[nn]], Prime[ Range[ nn]]}], PrimeQ]] (* Harvey P. Dale, Mar 19 2017 *)

Crossrefs

Cf. A000040, A000045, A100700.

Sequence in context: A124055 A137458 A079369 * A060383 A139044 A060442

Adjacent sequences: A102864 A102865 A102866 * A102868 A102869 A102870

Keyword

easy,sign

Author

Jonathan Vos Post, Mar 01 2005

Extensions

More terms from Harvey P. Dale, Mar 19 2017

Status

approved