A184902 Primes that are not factors of m^2 + m + 11 (A048058).

2, 3, 5, 7, 19, 29, 37, 61, 71, 73, 89, 113, 131, 137, 149, 151, 157, 163, 179, 191, 199, 211, 223, 227, 233, 241, 257, 263, 277, 313, 331, 347, 349, 373, 383, 389, 409, 419, 421, 433, 449, 457, 463, 467, 491, 499, 503, 521, 523, 571, 577

Offset: 1

Author

Zak Seidov, May 18 2011

Keywords

• nonn
• easy

Comments

The discriminant of this polynomial is -43. These are the primes that are not a square (mod 43). These primes are congruent to {2, 3, 5, 7, 8, 12, 18, 19, 20, 22, 26, 27, 28, 29, 30, 32, 33, 34, 37, 39, 42} (mod 43). - T. D. Noe, May 22 2011

Inert rational primes in the field Q(sqrt(-43)). - N. J. A. Sloane, Dec 25 2017

Links

• Zak Seidov, Table of n, a(n) for n = 1..5000
• Index to sequences related to decomposition of primes in quadratic fields

Crossrefs

Cf. A048058 (n^2 + n + 11), A048059 (primes of the form n^2 + n + 11), A048097 (n^2 + n + 11 is prime).

Programs

Mathematica

Reap[Do[p = Prime[n]; ta = Table[Mod[m(m + 1) + 11, p],{m, 0, p/2 + 1}]; If[FreeQ[ta, 0], Sow[p]], {n, 1000}]][[2, 1]]
Select[Prime[Range[100]], JacobiSymbol[#, 43] == -1 &] (* T. D. Noe, May 22 2011 *)

Formula

a(n) ~ 2n log n. - Charles R Greathouse IV, May 22 2011