A107145 -id:A107145 - cp's OEIS frontend

A139508 Primes of the form x^2 + 28x*y + y^2 for x and y nonnegative.

61, 181, 601, 829, 1069, 1249, 1381, 1429, 1609, 1621, 1741, 2029, 2089, 2161, 2341, 2389, 2521, 3121, 3169, 3181, 3301, 3709, 3769, 4021, 4261, 4549, 4729, 4801, 4861, 4969, 5209, 5281, 5521, 5581, 5641, 5749, 5821, 6301, 6361, 6421, 6529, 6709, 6829

Offset: 1

Artur Jasinski, Apr 24 2008

nonn

In base 12, the sequence is 51, 131, 421, 591, 751, 881, 971, 9E1, E21, E31, 1011, 1211, 1261, 1301, 1431, 1471, 1561, 1981, 1X01, 1X11, 1XE1, 2191, 2221, 23E1, 2571, 2771, 28X1, 2941, 2991, 2X61, 3021, 3081, 3241, 3291, 3321, 33E1, 3451, 3791, 3821, 3871, 3941, 3X71, 3E51, where X is 10 and E is 11. Moreover, the discriminant is 550. - Walter Kehowski, Jun 01 2008

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 = 28; 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*)

A139509 Primes of the form x^2 + 29x*y + y^2 for x and y nonnegative.

Original entry on oeis.org

31, 97, 211, 373, 547, 607, 661, 769, 877, 1051, 1087, 1123, 1249, 1279, 1303, 1423, 1597, 1657, 1663, 1693, 1741, 1777, 1861, 1867, 2143, 2179, 2251, 2341, 2467, 2539, 2791, 2857, 3229, 3259, 3319, 3331, 3373, 3511, 3541, 3643, 3697, 3769, 3823, 3877

Offset: 1

Artur Jasinski, Apr 24 2008

nonn

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 = 29; 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*)

A139510 Primes of the form x^2 + 30x*y + y^2 for x and y nonnegative.

Original entry on oeis.org

137, 193, 401, 617, 641, 953, 1009, 1129, 1289, 1297, 1801, 1913, 2129, 2137, 2377, 2473, 2657, 2713, 2801, 3049, 3257, 3313, 3329, 3593, 3889, 4001, 4057, 4153, 4201, 4337, 4649, 4657, 4729, 4817, 4937, 4993, 5009, 5153, 5209, 5441, 5657, 5849, 5881

Offset: 1

Artur Jasinski, Apr 24 2008

nonn

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 = 30; 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*)

A139511 Primes of the form x^2 + 31x*y + y^2 for x and y nonnegative.

Original entry on oeis.org

67, 103, 181, 199, 223, 313, 397, 463, 487, 499, 631, 643, 661, 691, 709, 883, 991, 1021, 1039, 1093, 1153, 1213, 1321, 1483, 1543, 1567, 1741, 1747, 1753, 1831, 1879, 2017, 2029, 2083, 2113, 2137, 2179, 2203, 2269, 2311, 2377, 2539, 2557, 2677, 2731

Offset: 1

Artur Jasinski, Apr 24 2008

nonn

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 = 31; 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*)

A139829 Primes of the form 4x^2+4xy+11y^2.

Original entry on oeis.org

11, 19, 59, 131, 139, 179, 211, 251, 331, 379, 419, 491, 499, 571, 619, 659, 691, 739, 811, 859, 971, 1019, 1051, 1091, 1171, 1259, 1291, 1451, 1459, 1499, 1531, 1571, 1579, 1619, 1699, 1811, 1931, 1979, 2011, 2099, 2131, 2179, 2251, 2339, 2371

Offset: 1

T. D. Noe, May 02 2008

Discriminant=-160. See A139827 for more information.

Also, primes of form u^2+10v^2 with odd v, while A107145 has even v. One can transform its form as (2x+y)^2+10y^2 (where y can only be odd) and the latter is x^2+10(2y)^2. This sequence has primes {11,19} mod 20 while the second has {1,9} mod 20 and together they are the primes x^2+10y^2 (A033201) which are {1,9,11,20} mod 20. [From Tito Piezas III, Jan 01 2009]

Vincenzo Librandi and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi]
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

[ p: p in PrimesUpTo(3000) | p mod 40 in {11, 19}]; // Vincenzo Librandi, Jul 29 2012

QuadPrimes2[4, -4, 11, 10000] (* see A106856 *)

The primes are congruent to {11, 19} (mod 40).

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A139508 Primes of the form x^2 + 28x*y + y^2 for x and y nonnegative.

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A139509 Primes of the form x^2 + 29x*y + y^2 for x and y nonnegative.

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A139510 Primes of the form x^2 + 30x*y + y^2 for x and y nonnegative.

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A139511 Primes of the form x^2 + 31x*y + y^2 for x and y nonnegative.

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A139829 Primes of the form 4x^2+4xy+11y^2.

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