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

Author

James Sellers, Feb 15 2000

Keywords

• easy
• nice
• nonn

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

Examples

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

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.

Crossrefs

Cf. A000045.

Programs

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

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 *)