A139506 Primes of the form x^2 + 26x*y + y^2 for x and y nonnegative.

193, 337, 457, 673, 1009, 1033, 1129, 1201, 1297, 1801, 1873, 2017, 2137, 2377, 2473, 2521, 2689, 2713, 2857, 3049, 3217, 3313, 3361, 3529, 3697, 3889, 4057, 4153, 4201, 4561, 4657, 4729, 4993, 5209, 5233, 5569, 5737, 5881, 6073, 6217, 6337, 6553, 6577

Offset: 1

Author

Artur Jasinski, Apr 24 2008

Keywords

• nonn

Comments

Also primes of the form x^2 + 168y^2. - T. D. Noe, Apr 29 2008

In base 12, the sequence is 141, 241, 321, 481, 701, 721, 7X1, 841, 901, 1061, 1101, 1201, 12X1, 1461, 1521, 1561, 1681, 16X1, 17X1, 1921, 1X41, 1E01, 1E41, 2061, 2181, 2301, 2421, 24X1, 2521, 2781, 2841, 28X1, 2X81, 3021, 3041, 3281, 33X1, 34X1, 3621, 3721, 3801, 3961, 3981, where X is 10 and E is 11. Moreover, the discriminant is 480. - Walter Kehowski, Jun 01 2008

Links

• N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Crossrefs

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

Cf. A139643.

Programs

Mathematica

a = {}; w = 26; k = 1; Do[Do[If[PrimeQ[n^2 + w*n*m + k*m^2], AppendTo[a, n^2 + w*n*m + k*m^2]], {n, m, 400}], {m, 1, 400}]; Union[a]

Formula

The primes are congruent to {1, 25, 121} (mod 168). - T. D. Noe, Apr 29 2008