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A050267
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Primes or negative values of primes in the sequence b(n) = 47*n^2 - 1701*n + 10181, n >= 0.
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37
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10181, 8527, 6967, 5501, 4129, 2851, 1667, 577, -419, -1321, -2129, -2843, -3463, -3989, -4421, -4759, -5003, -5153, -5209, -5171, -5039, -4813, -4493, -4079, -3571, -2969, -2273, -1483, -599, 379, 1451, 2617, 3877, 5231, 6679, 8221, 9857, 11587, 13411, 15329, 17341, 19447, 21647, 31387
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OFFSET
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1,1
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COMMENTS
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Terms are listed in the order of their appearance in sequence b.
This is a transformed version of the polynomial P(x) = 47*x^2 + 9*x - 5209 whose absolute value gives 43 distinct primes for -24 <= x <= 18, found by G. W. Fung in 1988. - Hugo Pfoertner, Dec 13 2019
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REFERENCES
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R. K. Guy, Unsolved Problems in Number Theory, 3rd ed., Springer, 2004 (ISBN 0-387-20860-7); see Section A17, p. 59.
Paulo Ribenboim, The Little Book of Bigger Primes, Second Edition, Springer-Verlag New York, 2004.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..1000
G. W. Fung and H. C. Williams, Quadratic polynomials which have a high density of prime values, Math. Comput. 55(191) (1990), 345-353.
Carlos Rivera, Problem 12: Prime producing polynomials, The Prime Puzzles & Problems Connection.
Eric Weisstein's World of Mathematics, Prime-Generating Polynomial.
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MATHEMATICA
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lst={}; Do[p=47*n^2-1701*n+10181; If[PrimeQ[p], AppendTo[lst, p]], {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jan 29 2009 *)
Select[Table[47n^2-1701n+10181, {n, 0, 50}], PrimeQ] (* Harvey P. Dale, Oct 03 2011 *)
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PROG
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(PARI) [n | n <- apply(m->47*m^2-1701*m+10181, [0..100]), isprime(abs(n))] \\ Charles R Greathouse IV, Jun 18 2017
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CROSSREFS
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Cf. A002383, A005471, A005846, A007635, A022464, A027753, A027755, A027758, A048059, A050267, A050268, A116206, A117081, A267252.
Sequence in context: A251274 A184205 A128878 * A102326 A216262 A243410
Adjacent sequences: A050264 A050265 A050266 * A050268 A050269 A050270
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KEYWORD
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sign,less
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AUTHOR
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Eric W. Weisstein
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EXTENSIONS
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Edited by N. J. A. Sloane, May 10 2007
Further edited by Klaus Brockhaus, Mar 20 2010
More terms (to distinguish from quadratic) from Charles R Greathouse IV, Jun 18 2017
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STATUS
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approved
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