A139502 Primes of the form x^2 + 22x*y + y^2 for x and y nonnegative.

241, 409, 601, 769, 1009, 1129, 1201, 1249, 1321, 1489, 1609, 1801, 2089, 2161, 2281, 2521, 2689, 3001, 3049, 3121, 3169, 3361, 3529, 3769, 3889, 4129, 4201, 4441, 4561, 4729, 4801, 4969, 5209, 5281, 5449, 5521, 5569, 5641, 5689, 5881, 6121, 6361, 6481

Offset: 1

Author

Artur Jasinski, Apr 24 2008

Keywords

• nonn
• easy

Comments

Also primes of the form x^2 + 120y^2. - T. D. Noe, Apr 29 2008

Also primes of the form x^2+240y^2. See A140633. - T. D. Noe, May 19 2008

In base 12, the sequence is 181, 2X1, 421, 541, 701, 7X1, 841, 881, 921, X41, E21, 1061, 1261, 1301, 13X1, 1561, 1681, 18X1, 1921, 1981, 1X01, 1E41, 2061, 2221, 2301, 2481, 2521, 26X1, 2781, 28X1, 2941, 2X61, 3021, 3081, 31X1, 3241, 3281, 3321, 3361, 34X1, 3661, 3821, 3901, where X is 10 and E is 11. Moreover, the discriminant is 340. - Walter Kehowski, Jun 01 2008

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Crossrefs

Cf. A139489, A007645, A068228, A007519, A033212, A033212, A107152, A107008, A033215, A107145, A139490, A139491.

Cf. A139643.

Programs

Magma

[ p: p in PrimesUpTo(7000) | p mod 120 in {1, 49}]; // Vincenzo Librandi, Jul 28 2012

Mathematica

QuadPrimes2[1, 0, 120, 10000] (* see A106856 *)

Formula

The primes are congruent to {1, 49} (mod 120). - T. D. Noe, Apr 29 2008