A141968 Primes congruent to 9 mod 28.

37, 149, 233, 317, 373, 401, 457, 541, 569, 653, 709, 821, 877, 1129, 1213, 1297, 1381, 1409, 1493, 1549, 1801, 1913, 1997, 2053, 2081, 2137, 2221, 2333, 2389, 2417, 2473, 2557, 2753, 2837, 3061, 3089, 3229, 3257, 3313, 3593, 3677, 3733, 3761, 3929, 4013, 4153

Offset

1,1

Comments

Also primes of the form x^2 - 7*y^2 (see Uspensky and Heaslet). - Stefano Spezia, Jun 29 2026

References

J. V. Uspensky and M. A. Heaslet, Elementary Number Theory, McGraw-Hill, NY, 1939, Exercise n. 2 at p. 368.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Formula

a(n) ~ 12n log n. - Charles R Greathouse IV, Jul 03 2016

Mathematica

Select[Prime[Range[1500]], MemberQ[{9}, Mod[#, 28]]&] (* Vincenzo Librandi, Aug 17 2012 *)
(* Alternative: *)
Select[Range[9, 4500, 28], PrimeQ] (* Harvey P. Dale, Mar 31 2022 *)

Prog

(Magma) [p: p in PrimesUpTo(5000) | p mod 28 eq 9 ]; // Vincenzo Librandi, Aug 17 2012
(PARI) is(n)=isprime(n) && n%28==9 \\ Charles R Greathouse IV, Jul 03 2016

Crossrefs

Cf. A000040.

Sequence in context: A157324 A251113 A251106 * A142656 A145898 A096700

Adjacent sequences: A141965 A141966 A141967 * A141969 A141970 A141971

Keyword

nonn,easy,changed

Author

N. J. A. Sloane, Jul 11 2008

Status

approved