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A053685
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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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2
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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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.
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REFERENCES
| Vladimir Drobot, On primes in the Fibonacci sequence, Fibonacci Quarterly 38, no. 1 (2000), 71-72.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
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EXAMPLE
| Note that 19 is prime and so is 2*19-1 or 37.
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MATHEMATICA
| okQ[n_]:=Module[{x=Mod[n, 5]}, PrimeQ[2n-1]&&MemberQ[{2, 4}, x]]; Select[Prime[Range[5, 500]], okQ] [From Harvey P. Dale, Jan. 14, 2011]
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CROSSREFS
| Cf. A000045.
Sequence in context: A158293 A107579 A050528 * A136063 A111441 A144594
Adjacent sequences: A053682 A053683 A053684 * A053686 A053687 A053688
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KEYWORD
| easy,nice,nonn
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AUTHOR
| James A. Sellers (sellersj(AT)math.psu.edu), Feb 15 2000
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