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A028871
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Primes of the form n^2 - 2.
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28
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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 first term 2, primes p such that continued fraction of (1+Sqrt[p])/2 have period 4. [From Artur Jasinski, Feb 03 2010]
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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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Nathaniel Johnston, Table of n, a(n) for n = 1..10000
P. De Geest, Palindromic Quasipronics of the form n(n+x)
Eric Weisstein's World of Mathematics, Near-Square Prime
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EXAMPLE
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a(3) = 23 = 5^2 - 2 = A028870(3)^2 - 2.
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MATHEMATICA
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lst={}; Do[s=n^2; If[PrimeQ[p=s-2], AppendTo[lst, p]], {n, 6!}]; lst [From Vladimir Joseph Stephan Orlovsky, Sep 26 2008]
aa = {}; Do[If[4 == Length[ContinuedFraction[(1 + Sqrt[Prime[m]])/2][[2]]], AppendTo[aa, Prime[m]]], {m, 1, 1000}]; aa (*Artur Jasinski*) [From 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
-- Reinhard Zumkeller, May 06 2013
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CROSSREFS
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Cf. A028870.
Cf. A010051, subsequence of A008865.
Sequence in context: A049552 A049572 A094786 * A053705 A049001 A049002
Adjacent sequences: A028868 A028869 A028870 * A028872 A028873 A028874
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KEYWORD
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nonn,changed
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AUTHOR
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Patrick De Geest
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STATUS
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approved
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