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A028871
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Primes of the form k^2 - 2.
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47
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2, 7, 23, 47, 79, 167, 223, 359, 439, 727, 839, 1087, 1223, 1367, 1847, 2207, 2399, 3023, 3719, 3967, 4759, 5039, 5623, 5927, 7919, 8647, 10607, 11447, 13687, 14159, 14639, 16127, 17159, 18223, 19319, 21023, 24023, 25919, 28559, 29927
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OFFSET
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1,1
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COMMENTS
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Except for the initial term, primes equal to the product of two consecutive even numbers minus 1. - Giovanni Teofilatto, Sep 24 2004
With exception of the first term 2, primes p such that continued fraction of (1+sqrt(p))/2 have period 4. - Artur Jasinski, Feb 03 2010
Subsequence of A094786. First primes q that are in A094786 but not here are 241, 3373, 6857, 19681, 29789, 50651, 300761, 371291, ...; q+2 are perfect powers m^k with odd k>1. - Zak Seidov, Dec 09 2014
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REFERENCES
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D. Shanks, Solved and Unsolved Problems in Number Theory, 2nd. ed., Chelsea, 1978, p. 31.
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LINKS
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FORMULA
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MAPLE
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select(isprime, [2, seq((2*n+1)^2-2, n=1..1000)]); # Robert Israel, Dec 09 2014
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MATHEMATICA
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aa = {}; Do[If[4 == Length[ContinuedFraction[(1 + Sqrt[Prime[m]])/2][[2]]], AppendTo[aa, Prime[m]]], {m, 1, 1000}]; aa (* Artur Jasinski, Feb 03 2010 *)
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PROG
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(PARI) list(lim)=select(n->isprime(n), vector(sqrtint(floor(lim)+2), k, k^2-2)) \\ Charles R Greathouse IV, Jul 25 2011
(Haskell)
a028871 n = a028871_list !! (n-1)
a028871_list = filter ((== 1) . a010051') a008865_list
(Magma) [p: p in PrimesUpTo(100000)| IsSquare(p+2)]; // Vincenzo Librandi, Jun 19 2014
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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