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

Author

Jonathan Vos Post, Mar 01 2005

Keywords

• easy
• sign

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

Examples

			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.
		

Crossrefs

Cf. A000040, A000045, A100700.

Programs

Mathematica

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

Formula

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

Extensions

More terms from Harvey P. Dale, Mar 19 2017