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Primes p > 7 which are congruent to 2 or 4 (mod 5) for which 2p-1 is also prime.
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%I #19 May 19 2019 01:43:47

%S 19,37,79,97,139,157,199,229,307,337,367,379,439,499,547,577,607,619,

%T 727,829,877,937,967,997,1009,1069,1237,1279,1297,1399,1429,1459,1609,

%U 1627,1657,1759,1867,2029,2089,2137,2179,2467,2539,2557,2617,2707,2719

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

%C 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.

%C Intersection of A047211 and A005382 without terms <= 7. - _Reinhard Zumkeller_, Oct 03 2012

%H T. D. Noe, <a href="/A053685/b053685.txt">Table of n, a(n) for n = 1..1000</a>

%H Vladimir Drobot, <a href="http://www.fq.math.ca/Scanned/38-1/drobot.pdf">On primes in the Fibonacci sequence</a>, Fib. Quart. 38 (1) (2000) 71.

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

%t 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 *)

%o (Haskell)

%o a053685 n = a053685_list !! (n-1)

%o a053685_list = dropWhile (<= 7) $ i a047211_list a005382_list where

%o i xs'@(x:xs) ys'@(y:ys) | x < y = i xs ys'

%o | x > y = i xs' ys

%o | otherwise = x : i xs ys

%o -- _Reinhard Zumkeller_, Oct 03 2012

%Y Cf. A000045.

%K easy,nice,nonn

%O 1,1

%A _James A. Sellers_, Feb 15 2000