A128878 Primes of the form 47*n^2 - 1701*n + 10181.

10181, 8527, 6967, 5501, 4129, 2851, 1667, 577, 379, 1451, 2617, 3877, 5231, 6679, 8221, 9857, 11587, 13411, 15329, 17341, 19447, 21647, 31387, 34057, 36821, 39679, 45677, 48817, 52051, 65927, 81307, 89561, 102647, 107197, 116579, 126337, 131357

Offset

1,1

Comments

Primes are given in the order in which they arise for increasing n.

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.

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.

References

R. K. Guy, Unsolved Problems in Number Theory, 3rd edition, Springer, 2004, ISBN 0-387-20860-7, Section A17, page 59.

Links

Table of n, a(n) for n=1..37.

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 and Problems Connection.

Example

47k^2 - 1701k + 10181 = 21647 for k = 42.

Mathematica

Select[Table[47*n^2 - 1701*n + 10181, {n, 0, 100}], # > 0 && PrimeQ[#] &] (* T. D. Noe, Aug 02 2011 *)

Crossrefs

Cf. A050267, A002383, A027753, A027755, A005471, A027758, A048059, A007635, A005846, A116206, A050268, A022464.

Sequence in context: A243974 A251274 A184205 * A050267 A102326 A216262

Adjacent sequences: A128875 A128876 A128877 * A128879 A128880 A128881

Keyword

nonn

Author

Douglas Winston (douglas.winston(AT)srupc.com), Apr 17 2007

Extensions

Edited by Klaus Brockhaus, Apr 22 2007 and by N. J. A. Sloane, May 05 2007 and May 06 2007

Status

approved