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A102867
Prime differences between k-th prime and k-th Fibonacci number.
0
-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
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
KEYWORD
easy,sign
AUTHOR
Jonathan Vos Post, Mar 01 2005
EXTENSIONS
More terms from Harvey P. Dale, Mar 19 2017
STATUS
approved