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A005850
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Primes p such that the NSW number A002315((p-1)/2) is prime.
(Formerly M2426)
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2
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3, 5, 7, 19, 29, 47, 59, 163, 257, 421, 937, 947, 1493, 1901, 6689, 8087, 9679, 28753, 79043, 129127, 145969, 165799, 168677, 170413, 172243
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listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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Some of the larger entries may only correspond to probable primes.
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REFERENCES
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P. Ribenboim, The Book of Prime Number Records. Springer-Verlag, NY, 2nd ed., 1989, p. 290.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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MATHEMATICA
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max = 10000 (* computation is very slow beyond this limit *); nc = Numerator[Convergents[Sqrt[2], max]]; Reap[Do[If[PrimeQ[n], If[PrimeQ[nc[[n]]], Print[n]; Sow[n]]] , {n, 3, max}]][[2, 1]] (* Jean-François Alcover, Oct 22 2012, after David Applegate *)
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PROG
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(PARI) is(n)=my(w=3+quadgen(32)); isprime(n) && n>2 && ispseudoprime(imag((1+w)*w^(n\2))) \\ Charles R Greathouse IV, Oct 19 2012
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CROSSREFS
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A099088 is a closely related sequence.
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KEYWORD
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nonn,nice,hard
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AUTHOR
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EXTENSIONS
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6689, 8087, 9679 reported by Warut Roonguthai on the PrimeForm mailing list.
28753 found by Andrew Walker (ajw01(AT)uow.edu.au), Jul 12 2001.
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STATUS
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approved
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