A053685 Primes p > 7 which are congruent to 2 or 4 (mod 5) for which 2p-1 is also prime.

19, 37, 79, 97, 139, 157, 199, 229, 307, 337, 367, 379, 439, 499, 547, 577, 607, 619, 727, 829, 877, 937, 967, 997, 1009, 1069, 1237, 1279, 1297, 1399, 1429, 1459, 1609, 1627, 1657, 1759, 1867, 2029, 2089, 2137, 2179, 2467, 2539, 2557, 2617, 2707, 2719

Offset

1,1

Comments

For such primes p, 2p-1 divides Fibonacci(p). Actually it is also true that (2m-1) divides Fibonacci(m) for *all* m > 7, m = 2 or 4 (mod 5) for which 2m-1 is prime.

Intersection of A047211 and A005382 without terms <= 7. - Reinhard Zumkeller, Oct 03 2012

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Vladimir Drobot, On primes in the Fibonacci sequence, Fib. Quart. 38 (1) (2000) 71.

Example

Note that 19 is prime and so is 2*19-1 or 37.

Mathematica

okQ[n_]:=Module[{x=Mod[n, 5]}, PrimeQ[2n-1]&&MemberQ[{2, 4}, x]]; Select[Prime[Range[5, 500]], okQ]  (* Harvey P. Dale, Jan 14 2011 *)

Prog

(Haskell)
a053685 n = a053685_list !! (n-1)
a053685_list = dropWhile (<= 7) $ i a047211_list a005382_list where
   i xs'@(x:xs) ys'@(y:ys) | x < y     = i xs ys'
                           | x > y     = i xs' ys
                           | otherwise = x : i xs ys
-- Reinhard Zumkeller, Oct 03 2012

Crossrefs

Cf. A000045.

Sequence in context: A257074 A357935 A299930 * A244111 A136063 A242979

Adjacent sequences: A053682 A053683 A053684 * A053686 A053687 A053688

Keyword

easy,nice,nonn

Author

James A. Sellers, Feb 15 2000

Status

approved