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Search: id:A002384
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| A002384 |
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Numbers n such that n^2 + n + 1 is prime.
(Formerly M0626 N0228)
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+0
23
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| 1, 2, 3, 5, 6, 8, 12, 14, 15, 17, 20, 21, 24, 27, 33, 38, 41, 50, 54, 57, 59, 62, 66, 69, 71, 75, 77, 78, 80, 89, 90, 99, 101, 105, 110, 111, 117, 119, 131, 138, 141, 143, 147, 150, 153, 155, 161, 162, 164, 167, 168, 173, 176, 188, 189, 192, 194, 203, 206, 209, 215
(list; graph; listen)
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OFFSET
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1,2
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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.
D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 46.
L. Poletti, Le serie dei numeri primi appartenente alle due forme quadratiche (A) n^2+n+1 e (B) n^2+n-1 ..., Atti della Reale Accademia Nazionale dei Lincei, Memorie della Classe di Scienze Fisiche, Matematiche e Naturali, s. 6. 3 (1929), 193-218.
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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T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
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a(n) = (A088503(n-1)-1)/2. - Chandler
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MATHEMATICA
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lst={}; Do[If[PrimeQ[n^2+n+1], AppendTo[lst, n]], {n, 10^4}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 20 2008]
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CROSSREFS
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Cf. A002383, A049407, A049408, A075723, A088503, A110284.
Sequence in context: A098491 A107947 A120768 this_sequence A096176 A002243 A094763
Adjacent sequences: A002381 A002382 A002383 this_sequence A002385 A002386 A002387
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Sep 07 2005
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