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Search: id:A002327
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| A002327 |
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Primes of form n^2 - n - 1.
(Formerly M3810 N1558)
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+0
22
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| 5, 11, 19, 29, 41, 71, 89, 109, 131, 181, 239, 271, 379, 419, 461, 599, 701, 811, 929, 991, 1259, 1481, 1559, 1721, 1979, 2069, 2161, 2351, 2549, 2861, 2969, 3079, 3191, 3539, 3659, 4159, 4289, 4421, 4691, 4969, 5851, 6971, 7309, 7481, 8009, 8741, 8929
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Also primes of form x*y + x + y or x*y - x - y, where x and y are two successive numbers. - Giovanni Teofilatto (g.teofilatto(AT)tiscalinet.it), May 12 2004
Equivalently primes p such that 4p+5 is square. - Giovanni Teofilatto (g.teofilatto(AT)tiscalinet.it), Sep 03 2005
Arithmetic numbers which are triangular, A003601(p)=A000217(k), p prime. sigma_1(p)/sigma_0(p)= k*(k+1)/2; sigma_r(p) divisor function, p prime, k integer. - Ctibor O. Zizka (ctibor.zizka(AT)seznam.cz), Jul 14 2008
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REFERENCES
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D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 46.
L. Poletti, Tavole di Numeri Primi Entro Limiti Diversi e Tavole Affini, Milan, 1920, p. 249.
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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FORMULA
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a(n) = A002328(n)^2 - A002328(n) - 1 = (A110013(n) - 5)/4. - Chandler
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MATHEMATICA
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a={}; Do[p=n^2-n-1; If[PrimeQ[p], AppendTo[a, p]], {n, 10^2}]; Print[a]; - Vladimir Orlovsky (4vladimir(AT)gmail.com), Apr 29 2008
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CROSSREFS
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Cf. A002328, A088502, A110013.
Cf. A003601, AA000217.
Sequence in context: A106071 A073847 A024833 this_sequence A078179 A045451 A100920
Adjacent sequences: A002324 A002325 A002326 this_sequence A002328 A002329 A002330
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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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