A140633 -id:A140633 - cp's OEIS frontend

A139830 Primes of the form 7x^2+6xy+7y^2.

7, 23, 47, 103, 127, 167, 223, 263, 367, 383, 463, 487, 503, 607, 647, 727, 743, 823, 863, 887, 967, 983, 1063, 1087, 1103, 1223, 1303, 1327, 1367, 1423, 1447, 1487, 1543, 1567, 1583, 1607, 1663, 1783, 1823, 1847, 2063, 2087, 2143, 2207, 2287

Offset: 1

T. D. Noe, May 02 2008

Discriminant=-160. See A139827 for more information.

Also primes of the forms 7x^2+2xy+23y^2 and 7x^2+4xy+12y^2. See A140633. - T. D. Noe, May 19 2008

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 {7, 23}]; // Vincenzo Librandi, Jul 29 2012

Union[QuadPrimes2[7, 6, 7, 10000], QuadPrimes2[7, -6, 7, 10000]] (* see A106856 *)

The primes are congruent to {7, 23} (mod 40).

A139847 Primes of the form 6x^2 + 6xy + 19y^2.

Original entry on oeis.org

19, 31, 139, 199, 271, 439, 619, 691, 811, 859, 1039, 1231, 1279, 1291, 1399, 1459, 1531, 1699, 1879, 1951, 2131, 2239, 2371, 2539, 2551, 2659, 2719, 2791, 2971, 3079, 3331, 3391, 3499, 3559, 3631, 3919, 4051, 4219, 4231, 4339, 4591, 4639

Offset: 1

T. D. Noe, May 02 2008

Discriminant = -420. See A139827 for more information.

Also primes of the forms 19x^2 + 12xy + 24y^2 and 19x^2 + 16xy + 31y^2. See A140633. - T. D. Noe, May 19 2008

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(6000) | p mod 420 in {19, 31, 139, 199, 271, 391}]; // Vincenzo Librandi, Jul 29 2012

QuadPrimes2[6, -6, 19, 10000] (* see A106856 *)

list(lim)=my(v=List(), s=[19, 31, 139, 199, 271, 391]); forprime(p=19, lim, if(setsearch(s, p%420), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Feb 10 2017

The primes are congruent to {19, 31, 139, 199, 271, 391} (mod 420).

A139856 Primes of the form 5x^2 + 24y^2.

Original entry on oeis.org

5, 29, 101, 149, 269, 389, 461, 509, 701, 821, 941, 1061, 1109, 1181, 1229, 1301, 1709, 1901, 1949, 2069, 2141, 2309, 2381, 2549, 2621, 2741, 2789, 2861, 2909, 3221, 3389, 3461, 3581, 3701, 3821, 3989, 4229, 4349, 4421, 5021, 5189, 5261

Offset: 1

T. D. Noe, May 02 2008

Discriminant=-480. See A139827 for more information.

Except for 5, also primes of the form 21x^2+6xy+29y^2. See A140633. - T. D. Noe, May 19 2008

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)

Cf. A140633.

[5] cat [ p: p in PrimesUpTo(6000) | p mod 120 in {29, 101}]; // Vincenzo Librandi, Jul 29 2012

QuadPrimes2[5, 0, 24, 10000] (* see A106856 *)

list(lim)=my(v=List(),w,t); for(x=1, sqrtint(lim\5), w=5*x^2; for(y=0, sqrtint((lim-w)\24), if(isprime(t=w+24*y^2), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 22 2017

Except for 5, the primes are congruent to {29, 101} (mod 120).

A139859 Primes of the form 11x^2+2xy+11y^2.

Original entry on oeis.org

11, 59, 131, 179, 251, 419, 491, 659, 971, 1019, 1091, 1259, 1451, 1499, 1571, 1619, 1811, 1931, 1979, 2099, 2339, 2411, 2459, 2531, 2579, 2699, 2819, 2939, 3011, 3251, 3299, 3371, 3491, 3539, 3659, 3779, 3851, 4019, 4091, 4139, 4211, 4259

Offset: 1

T. D. Noe, May 02 2008

Discriminant=-480. See A139827 for more information.

Also primes of the forms 11x^2+4xy+44y^2, 11x^2+10xy+35y^2 and 11x^2+8xy+56y^2. See A140633. - T. D. Noe, May 19 2008

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(6000) | p mod 120 in {11, 59}]; // Vincenzo Librandi, Jul 29 2012

Union[QuadPrimes2[11, 2, 11, 10000], QuadPrimes2[11, -2, 11, 10000]] (* see A106856 *)

The primes are congruent to {11, 59} (mod 120).

A139877 Primes of the form 8x^2+21y^2.

Original entry on oeis.org

29, 53, 149, 197, 317, 389, 557, 653, 701, 821, 1061, 1229, 1373, 1493, 1709, 1733, 1877, 1901, 1997, 2069, 2213, 2237, 2333, 2381, 2549, 2741, 2837, 2909, 3221, 3389, 3413, 3557, 3581, 3677, 3917, 4013, 4229, 4253, 4349, 4397, 4421, 4517

Offset: 1

T. D. Noe, May 02 2008

Discriminant=-672. See A139827 for more information.

Also primes of the form 29x^2+12xy+36y^2. See A140633. - T. D. Noe, May 19 2008

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(6000) | p mod 168 in {29, 53, 149}]; // Vincenzo Librandi, Jul 30 2012

QuadPrimes2[8, 0, 21, 10000] (* see A106856 *)

The primes are congruent to {29, 53, 149} (mod 168).

A139878 Primes of the form 8x^2+8xy+23y^2.

Original entry on oeis.org

23, 71, 191, 239, 263, 359, 431, 599, 743, 863, 911, 1031, 1103, 1367, 1439, 1583, 1607, 1871, 2039, 2087, 2111, 2207, 2423, 2447, 2543, 2591, 2711, 2879, 2927, 3119, 3623, 3719, 3767, 4127, 4271, 4391, 4463, 4799, 4943, 4967, 5231, 5279

Offset: 1

T. D. Noe, May 02 2008

Discriminant=-672. See A139827 for more information.

Also primes of the forms 23x^2+16xy+32y^2, 15x^2+6xy+23y^2 and 23x^2+4xy+44y^2. See A140633. - T. D. Noe, May 19 2008

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(6000) | p mod 168 in {23, 71, 95}]; // Vincenzo Librandi, Jul 30 2012

QuadPrimes2[8, -8, 23, 10000] (* see A106856 *)

The primes are congruent to {23, 71, 95} (mod 168).

A139879 Primes of the form 12x^2+12xy+17y^2.

Original entry on oeis.org

17, 41, 89, 257, 353, 521, 593, 761, 857, 881, 929, 1049, 1097, 1193, 1217, 1361, 1433, 1553, 1601, 1697, 1721, 1889, 2273, 2393, 2441, 2609, 2729, 2777, 2897, 3041, 3209, 3449, 3617, 3881, 4049, 4073, 4217, 4241, 4289, 4409, 4457, 4721

Offset: 1

T. D. Noe, May 02 2008

Discriminant=-672. See A139827 for more information.

Also primes of the forms 17x^2+10xy+41y^2 and 17x^2+4xy+20y^2. See A140633. - T. D. Noe, May 19 2008

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(6000) | p mod 168 in {17, 41, 89}]; // Vincenzo Librandi, Jul 30 2012

QuadPrimes2[12, -12, 17, 10000] (* see A106856 *)

The primes are congruent to {17, 41, 89} (mod 168).

Corrected and extended b-file - Ray Chandler, Jul 31 2014

A139923 Primes of the form 8x^2+39y^2.

Original entry on oeis.org

47, 71, 167, 239, 359, 383, 431, 479, 743, 839, 863, 983, 1103, 1151, 1319, 1367, 1487, 1607, 2039, 2087, 2111, 2351, 2399, 2423, 2543, 2663, 2711, 2879, 2927, 3023, 3167, 3191, 3359, 3671, 3863, 3911, 4127, 4271, 4583, 4751, 4799, 4919

Offset: 1

T. D. Noe, May 02 2008

Discriminant=-1248. See A139827 for more information.

Also primes of the form 15x^2+12xy+44y^2. See A140633. - T. D. Noe, May 19 2008

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(6000) | p mod 312 in [47, 71, 119, 167, 215, 239]]; // Vincenzo Librandi, Aug 01 2012

QuadPrimes2[8, 0, 39, 10000] (* see A106856 *)

The primes are congruent to {47, 71, 119, 167, 215, 239} (mod 312).

A139924 Primes of the form 8x^2+8xy+41y^2.

Original entry on oeis.org

41, 89, 137, 281, 353, 401, 449, 593, 617, 761, 929, 977, 1097, 1217, 1289, 1409, 1553, 1601, 1697, 1721, 1913, 2153, 2273, 2633, 2657, 2777, 2801, 2897, 2969, 3089, 3209, 3257, 3593, 3833, 3881, 4049, 4217, 4337, 4409, 4457, 4649, 4673

Offset: 1

T. D. Noe, May 02 2008

Discriminant=-1248. See A139827 for more information.
Also primes of the forms 32x^2+16xy+41y^2 and 20x^2+12xy+33y^2. See A140633. - T. D. Noe, May 19 2008
In base 12, the sequence is 35, 75, E5, 1E5, 255, 295, 315, 415, 435, 535, 655, 695, 775, 855, 8E5, 995, X95, E15, E95, EE5, 1135, 12E5, 1395, 1635, 1655, 1735, 1755, 1815, 1875, 1955, 1X35, 1X75, 20E5, 2275, 22E5, 2415, 2535, 2615, 2675, 26E5, 2835, 2855. Moreover, the discriminant is 880 and all primes are {35, 75, E5, 115, 1E5, 215} mod 220. - Walter Kehowski, May 31 2008

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(6000) | p mod 312 in [41, 89, 137, 161, 281, 305]]; // Vincenzo Librandi, Aug 01 2012

QuadPrimes2[8, -8, 41, 10000] (* see A106856 *)

The primes are congruent to {41, 89, 137, 161, 281, 305} (mod 312).

A139988 Primes of the form 8x^2+105y^2.

Original entry on oeis.org

113, 137, 233, 617, 953, 977, 1913, 2153, 2297, 2417, 2633, 2657, 2753, 3137, 3257, 3593, 3833, 4337, 4673, 4817, 4937, 5153, 5273, 5657, 6113, 6353, 6833, 6857, 7193, 7457, 7673, 7793, 8297, 8513, 8537, 9137, 9377, 9473, 9857, 10193, 10313

Offset: 1

T. D. Noe, May 02 2008

Discriminant=-3360. See A139827 for more information.

Also primes of the form 32x^2+24xy+57y^2. See A140633. - T. D. Noe, May 19 2008

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(11000) | p mod 840 in [113, 137, 233, 473, 617, 737]]; // Vincenzo Librandi, Aug 03 2012

QuadPrimes2[8, 0, 105, 10000] (* see A106856 *)

The primes are congruent to {113, 137, 233, 473, 617, 737} (mod 840).

cp's OEIS Frontend

A139830 Primes of the form 7x^2+6xy+7y^2.

Views

Author

Keywords

Comments

Links

Programs

Magma

Mathematica

Formula

A139847 Primes of the form 6x^2 + 6xy + 19y^2.

Views

Author

Keywords

Comments

Links

Programs

Magma

Mathematica

PARI

Formula

A139856 Primes of the form 5x^2 + 24y^2.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

A139859 Primes of the form 11x^2+2xy+11y^2.

Views

Author

Keywords

Comments

Links

Programs

Magma

Mathematica

Formula

A139877 Primes of the form 8x^2+21y^2.

Views

Author

Keywords

Comments

Links

Programs

Magma

Mathematica

Formula

A139878 Primes of the form 8x^2+8xy+23y^2.

Views

Author

Keywords

Comments

Links

Programs

Magma

Mathematica

Formula

A139879 Primes of the form 12x^2+12xy+17y^2.

Views

Author

Keywords

Comments

Links

Programs

Magma

Mathematica

Formula

Extensions

A139923 Primes of the form 8x^2+39y^2.

Views

Author

Keywords

Comments