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A002327
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Primes of the form k^2 - k - 1.
(Formerly M3810 N1558)
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40
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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
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OFFSET
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1,1
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COMMENTS
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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, May 12 2004
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, 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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LINKS
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FORMULA
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MAPLE
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MATHEMATICA
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Select[Table[n^2-n-1, {n, 100}], PrimeQ] (* Harvey P. Dale, May 03 2011 *)
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PROG
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(PARI) list(lim)=my(v=List(), p); forstep(n=5, sqrtint(4*lim+5), 2, if(isprime(p=(n^2-5)/4), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Oct 10 2023
(Magma) [ a: n in [0..150] | IsPrime(a) where a is n^2 - n - 1 ]; // Vincenzo Librandi, Aug 01 2011
(Haskell)
a002327 n = a002327_list !! (n-1)
a002327_list = filter ((== 1) . a010051') a028387_list
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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