A107132 -id:A107132 - cp's OEIS frontend

A107142 Primes of the form x^2 + 36y^2.

37, 61, 157, 193, 313, 349, 373, 397, 433, 577, 601, 613, 661, 673, 769, 853, 877, 937, 997, 1021, 1069, 1201, 1297, 1321, 1429, 1549, 1657, 1693, 1741, 1789, 1801, 1861, 1933, 1993, 2053, 2137, 2269, 2293, 2389, 2437, 2473, 2521, 2593, 2749

Offset: 1

T. D. Noe, May 13 2005

Discriminant = -144. See A107132 for more information.

These appear to be the same as Glaisher's 1889 list of primes == 1 mod 12 that have "positive character". - N. J. A. Sloane, Jul 30 2015

J. W. L. Glaisher, On the square of Euler's series, Proc. London Math. Soc., 21 (1889), 182-194.

Vincenzo Librandi and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi]
S. R. Finch, Powers of Euler's q-Series, (arXiv:math.NT/0701251).
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

QuadPrimes2[1, 0, 36, 10000] (* see A106856 *)

list(lim)=my(v=List(),w,t); for(x=1, sqrtint(lim\1), w=x^2; for(y=1, sqrtint((lim-w)\36), if(isprime(t=w+36*y^2), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 09 2017

A107143 Primes of the form 2x^2 + 19y^2.

Original entry on oeis.org

2, 19, 37, 173, 179, 181, 269, 307, 509, 547, 563, 683, 971, 1093, 1123, 1171, 1229, 1381, 1523, 1571, 1579, 1627, 1637, 1667, 1877, 1931, 1933, 2083, 2339, 2371, 2389, 2621, 2731, 2749, 2789, 2909, 3061, 3067, 3109, 3181, 3221, 3229, 3371

Offset: 1

T. D. Noe, May 13 2005

Discriminant = -152. See A107132 for more information.

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)

QuadPrimes2[2, 0, 19, 10000] (* see A106856 *)

list(lim)=my(v=List(),w,t); for(x=0, sqrtint(lim\2), w=2*x^2; for(y=0, sqrtint((lim-w)\19), if(isprime(t=w+19*y^2), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 09 2017

A107146 Primes of the form 6x^2 + 7y^2.

Original entry on oeis.org

7, 13, 31, 61, 103, 157, 181, 199, 223, 229, 271, 349, 367, 397, 439, 607, 661, 727, 733, 829, 853, 997, 1021, 1039, 1063, 1069, 1231, 1237, 1279, 1399, 1447, 1543, 1567, 1669, 1693, 1741, 1783, 1861, 1879, 1951, 2029, 2239, 2287, 2341, 2383

Offset: 1

T. D. Noe, May 13 2005

Discriminant = -168. See A107132 for more information.

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. A139827.

[ p: p in PrimesUpTo(3000) | p mod 168 in {7, 13, 31, 55, 61, 103, 157} ]; // Vincenzo Librandi, Jul 24 2012

QuadPrimes2[6, 0, 7, 10000] (* see A106856 *)

list(lim)=my(v=List([7]), s=[13, 31, 55, 61, 103, 157]); forprime(p=13, lim, if(setsearch(s, p%168), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Feb 09 2017

The primes are congruent to {7, 13, 31, 55, 61, 103, 157} (mod 168). - T. D. Noe, May 02 2008

A107148 Primes of the form 2x^2 + 21y^2.

Original entry on oeis.org

2, 23, 29, 53, 71, 149, 191, 197, 239, 263, 317, 359, 389, 431, 557, 599, 653, 701, 743, 821, 863, 911, 1031, 1061, 1103, 1229, 1367, 1373, 1439, 1493, 1583, 1607, 1709, 1733, 1871, 1877, 1901, 1997, 2039, 2069, 2087, 2111, 2207, 2213, 2237

Offset: 1

T. D. Noe, May 13 2005

Discriminant = -168. See A107132 for more information.

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. A139827.

[ p: p in PrimesUpTo(3000) | p mod 168 in {2, 23, 29, 53, 71, 95, 149} ]; // Vincenzo Librandi, Jul 24 2012

QuadPrimes2[2, 0, 21, 10000] (* see A106856 *)

list(lim)=my(v=List([2]), s=[23, 29, 53, 71, 95, 149]); forprime(p=23, lim, if(setsearch(s, p%168), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Feb 09 2017

The primes are congruent to {2, 23, 29, 53, 71, 95, 149} (mod 168). - T. D. Noe, May 02 2008

A107149 Primes of the form 4x^2 + 11y^2.

Original entry on oeis.org

11, 47, 103, 163, 199, 311, 419, 499, 587, 599, 683, 863, 883, 907, 911, 991, 1087, 1123, 1291, 1307, 1367, 1439, 1543, 1567, 1571, 1699, 1907, 2003, 2039, 2539, 2579, 2671, 2731, 2803, 2843, 2927, 3191, 3259, 3323, 3391, 3463, 3499, 3623

Offset: 1

T. D. Noe, May 13 2005

Discriminant = -176. See A107132 for more information.

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)

QuadPrimes2[4, 0, 11, 10000] (* see A106856 *)

list(lim)=my(v=List(),w,t); for(x=0, sqrtint(lim\4), w=4*x^2; for(y=1, sqrtint((lim-w)\11), if(isprime(t=w+11*y^2), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 09 2017

A107150 Primes of the form x^2 + 44y^2.

Original entry on oeis.org

53, 257, 269, 397, 401, 421, 617, 757, 773, 929, 1021, 1109, 1181, 1237, 1433, 1609, 1621, 1697, 1753, 1873, 2069, 2113, 2237, 2381, 2621, 2729, 2777, 2797, 2897, 2953, 3041, 3257, 3433, 3613, 3677, 3701, 3733, 3793, 3853, 3877, 4013, 4093

Offset: 1

T. D. Noe, May 13 2005

Discriminant = -176. See A107132 for more information.

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)

QuadPrimes2[1, 0, 44, 10000] (* see A106856 *)

list(lim)=my(v=List(),w,t); for(x=1, sqrtint(lim\1), w=x^2; for(y=0, sqrtint((lim-w)\44), if(isprime(t=w+44*y^2), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 09 2017

A107153 Primes of the form 2x^2 + 23y^2.

Original entry on oeis.org

2, 23, 31, 41, 73, 151, 223, 239, 257, 311, 449, 577, 593, 599, 601, 607, 647, 673, 719, 823, 863, 929, 967, 991, 1087, 1129, 1153, 1223, 1289, 1297, 1327, 1481, 1543, 1559, 1823, 1871, 1889, 1913, 2063, 2129, 2143, 2377, 2441, 2473, 2657, 2663

Offset: 1

T. D. Noe, May 13 2005

Discriminant = -184. See A107132 for more information.

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)

QuadPrimes2[2, 0, 23, 10000] (* see A106856 *)

list(lim)=my(v=List(),w,t); for(x=0, sqrtint(lim\2), w=2*x^2; for(y=0, sqrtint((lim-w)\23), if(isprime(t=w+23*y^2), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 09 2017

A107155 Primes of the form x^2 + 49y^2.

Original entry on oeis.org

53, 113, 149, 193, 197, 277, 317, 373, 421, 449, 457, 541, 557, 809, 821, 953, 1009, 1117, 1229, 1289, 1409, 1481, 1493, 1549, 1597, 1709, 1789, 1801, 1873, 1877, 1901, 1933, 2053, 2153, 2221, 2293, 2377, 2381, 2389, 2417, 2437, 2521, 2549

Offset: 1

T. D. Noe, May 13 2005

Discriminant = -196. See A107132 for more information.

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)

QuadPrimes2[1, 0, 49, 10000] (* see A106856 *)

list(lim)=my(v=List(),w,t); for(x=1, sqrtint(lim\1), w=x^2; for(y=1, sqrtint((lim-w)\49), if(isprime(t=w+49*y^2), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 09 2017

A107156 Primes of the form 2x^2 + 25y^2.

Original entry on oeis.org

2, 43, 97, 227, 233, 257, 313, 353, 467, 563, 617, 643, 673, 787, 907, 947, 1193, 1283, 1297, 1483, 1777, 1873, 1907, 2027, 2083, 2153, 2203, 2267, 2273, 2377, 2417, 2617, 2683, 2803, 2963, 3067, 3083, 3187, 3217, 3313, 3593, 3673, 3907

Offset: 1

T. D. Noe, May 13 2005

Discriminant = -200. See A107132 for more information.

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)

QuadPrimes2[2, 0, 25, 10000] (* see A106856 *)

list(lim)=my(v=List(),w,t); for(x=1, sqrtint(lim\2), w=2*x^2; for(y=0, sqrtint((lim-w)\25), if(isprime(t=w+25*y^2), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 09 2017

A107157 Primes of the form x^2 + 50y^2.

Original entry on oeis.org

59, 131, 281, 491, 499, 571, 619, 641, 739, 809, 811, 881, 929, 1259, 1289, 1291, 1571, 1721, 1801, 1889, 1979, 2089, 2131, 2161, 2339, 2459, 2531, 2659, 2801, 2851, 3169, 3209, 3259, 3299, 3449, 3539, 3851, 3929, 3931, 4019, 4049, 4051

Offset: 1

T. D. Noe, May 13 2005

Discriminant = -200. See A107132 for more information.

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)

QuadPrimes2[1, 0, 50, 10000] (* see A106856 *)

list(lim)=my(v=List(),w,t); for(x=1, sqrtint(lim\1), w=x^2; for(y=1, sqrtint((lim-w)\50), if(isprime(t=w+50*y^2), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 09 2017

cp's OEIS Frontend

A107142 Primes of the form x^2 + 36y^2.

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A107143 Primes of the form 2x^2 + 19y^2.

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A107146 Primes of the form 6x^2 + 7y^2.

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A107148 Primes of the form 2x^2 + 21y^2.

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A107149 Primes of the form 4x^2 + 11y^2.

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A107150 Primes of the form x^2 + 44y^2.

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A107153 Primes of the form 2x^2 + 23y^2.

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A107155 Primes of the form x^2 + 49y^2.

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