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%I #43 Dec 04 2024 10:34:39
%S 10181,8527,6967,5501,4129,2851,1667,577,-419,-1321,-2129,-2843,-3463,
%T -3989,-4421,-4759,-5003,-5153,-5209,-5171,-5039,-4813,-4493,-4079,
%U -3571,-2969,-2273,-1483,-599,379,1451,2617,3877,5231,6679,8221,9857,11587,13411,15329,17341,19447,21647,31387
%N Primes or negative values of primes in the sequence b(n) = 47*n^2 - 1701*n + 10181, n >= 0.
%C Terms are listed in the order of their appearance in sequence b.
%C 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
%D R. K. Guy, Unsolved Problems in Number Theory, 3rd ed., Springer, 2004 (ISBN 0-387-20860-7); see Section A17, p. 59.
%D Paulo Ribenboim, The Little Book of Bigger Primes, Second Edition, Springer-Verlag New York, 2004.
%H Vincenzo Librandi, <a href="/A050267/b050267.txt">Table of n, a(n) for n = 1..1000</a>
%H G. W. Fung and H. C. Williams, <a href="https://www.jstor.org/stable/2008810">Quadratic polynomials which have a high density of prime values</a>, Math. Comput. 55(191) (1990), 345-353.
%H Carlos Rivera, <a href="http://www.primepuzzles.net/problems/prob_012.htm">Problem 12: Prime producing polynomials</a>, The Prime Puzzles & Problems Connection.
%H Jitender Singh, <a href="https://arxiv.org/abs/2411.18366">Prime numbers and factorization of polynomials</a>, arXiv:2411.18366 [math.NT], 2024.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Prime-GeneratingPolynomial.html">Prime-Generating Polynomial</a>.
%t 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 *)
%t Select[Table[47n^2-1701n+10181,{n,0,50}],PrimeQ] (* _Harvey P. Dale_, Oct 03 2011 *)
%o (PARI) [n | n <- apply(m->47*m^2-1701*m+10181, [0..100]), isprime(abs(n))] \\ _Charles R Greathouse IV_, Jun 18 2017
%Y Cf. A002383, A005471, A005846, A007635, A022464, A027753, A027755, A027758, A048059, A050267, A050268, A116206, A117081, A267252.
%K sign,less
%O 1,1
%A _Eric W. Weisstein_
%E Edited by _N. J. A. Sloane_, May 10 2007
%E Further edited by _Klaus Brockhaus_, Mar 20 2010
%E More terms (to distinguish from quadratic) from _Charles R Greathouse IV_, Jun 18 2017