A139512 -id:A139512 - cp's OEIS frontend

A139493 Primes of the form x^2 + 9x*y + y^2 for x and y nonnegative.

11, 23, 37, 53, 67, 71, 113, 137, 163, 179, 191, 317, 331, 379, 389, 401, 421, 443, 449, 463, 487, 499, 599, 617, 631, 641, 653, 683, 709, 751, 757, 823, 863, 883, 907, 911, 947, 977, 991, 1061, 1087, 1093, 1103, 1171, 1213, 1303, 1367, 1373, 1409, 1423

Offset: 1

Artur Jasinski, Apr 24 2008

nonn

This is a member of the family of sequences of primes of the forms x^2 + kxy + y^2.

See for k=1 A007645 = x^2+3y^2, k=2 squares no primes, k=3 A038872, k=4 A068228 = x^2+9y^2, k=5 A139492, k=6 A007519 = x^2+8y^2, k=7 A033212 = x^2+15y^2, k=8 A107152 = x^2+45y^2, k=9 A139493, k=10 A107008 = x^2+24y^2, k=11 A139494, k=12 A139495, k=13 A139496, k=14* = 10 A107008 = x^2+24y^2, k=15 A139497, k=16 A033215 = x^2+21y^2, k=17 A139498, k=18 A107145 = x^2+40y^2, k=19 A139499, k=20 A139500, k=21 A139501, k=22 A139502, k=23 A139503, k=24 A139504, k=25 A139505, k=26,A139506, k=27 A139507, k=28 A139508, k=29 A139509, k=30 A139510, k=31 A139511, k=32 A139512

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

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

a = {}; w = 9; 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] (*Artur Jasinski*)

A139539 Indices of numbers of form 12k+1 which are prime and have representation x^2+32xy+y^2.

Original entry on oeis.org

19, 29, 34, 35, 55, 64, 69, 85, 89, 104, 115, 119, 129, 149, 150, 155, 174, 180, 189, 199, 250, 255, 259, 265, 269, 289, 324, 335, 344, 350, 370, 405, 409, 425, 454, 460, 489, 490, 510, 539, 540, 544, 565, 579, 580, 609, 614, 624, 629, 630, 639, 675, 680, 684

Offset: 1

Artur Jasinski, Apr 25 2008

nonn

Cf. A068228, A139512.

A139540 Indices of primes of the form 12k+1 which have representation x^2+32xy+y^2.

Original entry on oeis.org

10, 15, 18, 19, 26, 31, 32, 38, 40, 48, 51, 52, 55, 65, 66, 67, 74, 77, 79, 84, 100, 103, 104, 107, 109, 117, 131, 132, 135, 138, 143, 154, 155, 161, 169, 170, 182, 183, 187, 198, 199, 200, 208, 212, 213, 222, 225, 229, 231, 232, 235, 247, 248, 249, 255, 258

Offset: 1

Artur Jasinski, Apr 25 2008

nonn

Cf. A068228, A139512, A139539.

cp's OEIS Frontend

A139493 Primes of the form x^2 + 9x*y + y^2 for x and y nonnegative.

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A139539 Indices of numbers of form 12k+1 which are prime and have representation x^2+32xy+y^2.

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Author

Keywords

Crossrefs

A139540 Indices of primes of the form 12k+1 which have representation x^2+32xy+y^2.

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Author

Keywords

Crossrefs