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%I #17 Jun 17 2021 04:38:46
%S 10181,8527,6967,5501,4129,2851,1667,577,379,1451,2617,3877,5231,6679,
%T 8221,9857,11587,13411,15329,17341,19447,21647,31387,34057,36821,
%U 39679,45677,48817,52051,65927,81307,89561,102647,107197,116579,126337,131357
%N Primes of the form 47*n^2 - 1701*n + 10181.
%C Primes are given in the order in which they arise for increasing n.
%C Polynomial generates 22 primes for 0 <= n <= 42, i.e., for n = 0, 1, 2, 3, 4, 5, 6, 7, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42.
%C If the definition is replaced by "Numbers n of the form 47*k^2 - 1701*k + 10181 such that either n or -n is a prime" we get (essentially) A050267.
%D R. K. Guy, Unsolved Problems in Number Theory, 3rd edition, Springer, 2004, ISBN 0-387-20860-7, Section A17, page 59.
%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 and Problems Connection.
%e 47k^2 - 1701k + 10181 = 21647 for k = 42.
%t Select[Table[47*n^2 - 1701*n + 10181, {n, 0, 100}], # > 0 && PrimeQ[#] &] (* _T. D. Noe_, Aug 02 2011 *)
%Y Cf. A050267, A002383, A027753, A027755, A005471, A027758, A048059, A007635, A005846, A116206, A050268, A022464.
%K nonn
%O 1,1
%A Douglas Winston (douglas.winston(AT)srupc.com), Apr 17 2007
%E Edited by _Klaus Brockhaus_, Apr 22 2007 and by _N. J. A. Sloane_, May 05 2007 and May 06 2007
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