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A002642
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Numbers n such that (n^2 + n + 1)/13 is prime.
(Formerly M4606 N1131)
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2
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9, 29, 35, 42, 48, 113, 120, 126, 152, 185, 204, 224, 237, 243, 276, 302, 308, 321, 341, 386, 399, 419, 432, 477, 503, 510, 516, 542, 549, 588, 633, 659, 666, 705, 731, 770, 776, 783, 789, 815, 848, 854, 887, 906, 932, 945, 965, 978
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OFFSET
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1,1
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COMMENTS
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All terms are congruent to 3 or 9 (mod 13). [Bruno Berselli, Sep 26 2012]
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REFERENCES
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A. J. C. Cunningham, Binomial Factorisations, Vols. 1-9, Hodgson, London, 1923-1929; see Vol. 1, pp. 245-259.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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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Vincenzo Librandi, Table of n, a(n) for n = 1..1000
A. J. C. Cunningham, Binomial Factorisations, Vols. 1-9, Hodgson, London, 1923-1929. [Annotated scans of a few pages from Volumes 1 and 2]
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MATHEMATICA
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Select[Range[1000], PrimeQ[(#^2 + # + 1)/13]&] (* Vincenzo Librandi, Sep 25 2012 *)
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PROG
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(PARI) forstep(n=9, 1e4, [7, 6], if(isprime((n^2+n+1)/13), print1(n", "))) \\ Charles R Greathouse IV, Sep 25 2012
(Magma)
I:=[m: m in [1..1000] | m mod 13 in [3, 9]];
[n: n in I | IsPrime( (n^2 + n + 1) div 13 )];
// Bruno Berselli, Sep 26 2012
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CROSSREFS
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Sequence in context: A205144 A258483 A044976 * A032700 A322946 A350963
Adjacent sequences: A002639 A002640 A002641 * A002643 A002644 A002645
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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