A139827 -id:A139827 - cp's OEIS frontend

A106889 Primes of the form 2x^2 + 5y^2.

2, 5, 7, 13, 23, 37, 47, 53, 103, 127, 157, 167, 173, 197, 223, 263, 277, 293, 317, 367, 373, 383, 397, 463, 487, 503, 557, 607, 613, 647, 653, 677, 727, 733, 743, 757, 773, 797, 823, 853, 863, 877, 887, 967, 983, 997, 1013, 1063, 1087, 1093, 1103, 1117

Offset: 1

T. D. Noe, May 09 2005

Discriminant = -40.

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. Primes in A020674.

QuadPrimes2[2, 0, 5, 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)\5), if(isprime(t=w+5*y^2), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 09 2017

The primes are congruent to {2, 5, 7, 13, 23, 37} (mod 40). - T. D. Noe, May 02 2008

A107169 Primes of the form 3x^2 + 20y^2.

Original entry on oeis.org

3, 23, 47, 83, 107, 167, 227, 263, 347, 383, 443, 467, 503, 563, 587, 647, 683, 743, 827, 863, 887, 947, 983, 1103, 1163, 1187, 1223, 1283, 1307, 1367, 1427, 1487, 1523, 1583, 1607, 1667, 1787, 1823, 1847, 1907, 2003, 2027, 2063, 2087, 2207

Offset: 1

T. D. Noe, May 13 2005

Discriminant = -240. See A107132 for more information.

Except for 3, also primes of the forms 2x^2 + 2xy + 23y^2 (A139831) and 8x^2 + 4xy + 23y^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. A139827.

[3] cat [p: p in PrimesUpTo(3000) | p mod 60 in [23, 47]]; // Vincenzo Librandi, Jul 25 2012

QuadPrimes2[3, 0, 20, 10000] (* see A106856 *)

list(lim)=my(v=List([3]),t); forprime(p=23,lim, t=p%60; if(t==23||t==47, listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Feb 10 2017

Except for 3, the primes are congruent to {23, 47} (mod 60). - T. D. Noe, May 02 2008

A139855 Primes of the form 4x^2+4xy+31y^2.

Original entry on oeis.org

31, 79, 151, 199, 271, 439, 631, 751, 919, 991, 1039, 1231, 1279, 1399, 1471, 1759, 1831, 1879, 1951, 1999, 2239, 2311, 2551, 2671, 2719, 2791, 3079, 3271, 3319, 3391, 3511, 3559, 3631, 3919, 4111, 4159, 4231, 4519, 4591, 4639, 4759, 4831

Offset: 1

T. D. Noe, May 02 2008

Discriminant = -480. See A139827 for more information.
Also primes of the form 15x^2+16y^2, which has discriminant = -960. - T. D. Noe, May 07 2008
Also primes of the form 16x^2+8xy+31y^2, which has discriminant = -1920. See A140633. - T. D. Noe, May 19 2008

Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi]
William C. Jagy and Irving Kaplansky, Positive definite binary quadratic forms that represent the same primes [Cached copy] See item 14 in Table II.
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 {31, 79}]; // Vincenzo Librandi, Jul 29 2012

QuadPrimes2[4, -4, 31, 10000] (* see A106856 *)

The primes are congruent to {31, 79} (mod 120).

A139857 Primes of the form 8x^2 + 15y^2.

Original entry on oeis.org

23, 47, 167, 263, 383, 503, 647, 743, 863, 887, 983, 1103, 1223, 1367, 1487, 1583, 1607, 1823, 1847, 2063, 2087, 2207, 2423, 2447, 2543, 2663, 2687, 2903, 2927, 3023, 3167, 3407, 3527, 3623, 3767, 3863, 4007, 4127, 4463, 4583, 4703, 4943

Offset: 1

T. D. Noe, May 02 2008

Discriminant= = -480. See A139827 for more information.
Also primes of the form 12x^2 + 12xy + 23y^2, which has discriminant = -960. - T. D. Noe, May 07 2008
Also primes of the forms 23x^2 + 22xy + 47y^2 and 23x^2 + 8xy + 32y^2. See A140633. - T. D. Noe, May 19 2008

Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi]
William C. Jagy and Irving Kaplansky, Positive definite binary quadratic forms that represent the same primes [Cached copy] See Table II.
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 {23, 47}]; // Vincenzo Librandi, Jul 29 2012

QuadPrimes2[8, 0, 15, 10000] (* see A106856 *)

list(lim)=my(v=List(),w,t); for(x=1, sqrtint(lim\8), w=8*x^2; for(y=1, sqrtint((lim-w)\15), if(isprime(t=w+15*y^2), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 22 2017

The primes are congruent to {23, 47} (mod 120).

A139858 Primes of the form 8x^2+8xy+17y^2.

Original entry on oeis.org

17, 113, 137, 233, 257, 353, 593, 617, 857, 953, 977, 1097, 1193, 1217, 1433, 1553, 1697, 1913, 2153, 2273, 2297, 2393, 2417, 2633, 2657, 2753, 2777, 2897, 3137, 3257, 3593, 3617, 3833, 4073, 4217, 4337, 4457, 4673, 4793, 4817, 4937, 5153

Offset: 1

T. D. Noe, May 02 2008

Discriminant=-480. See A139827 for more information.
Also primes of the form 17x^2+14xy+17y^2, which has discriminant=-960. - T. D. Noe, May 07 2008
Also primes of the forms 17x^2+16xy+32y^2 and 17x^2+6xy+57y^2. See A140633. - T. D. Noe, May 19 2008

Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi]
William C. Jagy and Irving Kaplansky, Positive definite binary quadratic forms that represent the same primes [Cached copy] See Item 15 of Table II.
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 {17, 113}]; // Vincenzo Librandi, Jul 29 2012

QuadPrimes2[8, -8, 17, 10000] (* see A106856 *)

The primes are congruent to {17, 113} (mod 120).

A007639 Primes of form 2n^2 - 2n + 19.

Original entry on oeis.org

19, 23, 31, 43, 59, 79, 103, 131, 163, 199, 239, 283, 331, 383, 439, 499, 563, 631, 859, 1031, 1123, 1319, 1423, 1531, 1759, 1879, 2003, 2131, 2399, 2539, 2683, 3299, 3463, 3631, 3803, 4159, 4723, 4919, 5119, 5323, 5531, 5743, 6863, 7583, 8599

Offset: 1

N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
H. Dubner, Generalized Cullen numbers, J. Rec. Math., 21 (No. 3, 1989), 190-191. (Annotated scanned copy)

Cf. A139827.

[a: n in [1..60] | IsPrime(a) where a is 2*n^2-2*n+19]; // Vincenzo Librandi, Mar 20 2013

Select[Table[2n^2-2n+19,{n,90}],PrimeQ] (* Harvey P. Dale, Dec 19 2011 *)

The primes are congruent to {2, 15, 19, 23, 31, 35, 39, 43, 51, 55, 59, 79, 87, 91, 103, 119, 131, 135, 143} (mod 148). - T. D. Noe, May 02 2008

A107135 Primes of the form 5x^2 + 6y^2.

Original entry on oeis.org

5, 11, 29, 59, 101, 131, 149, 179, 251, 269, 389, 419, 461, 491, 509, 659, 701, 821, 941, 971, 1019, 1061, 1091, 1109, 1181, 1229, 1259, 1301, 1451, 1499, 1571, 1619, 1709, 1811, 1901, 1931, 1949, 1979, 2069, 2099, 2141, 2309, 2339, 2381, 2411

Offset: 1

T. D. Noe, May 13 2005

Discriminant = -120. See A107132 for more information.

Except for 5, also primes of the form 11x^2 + 4xy + 14y^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. A139827.

[ p: p in PrimesUpTo(3000) | p mod 120 in {5, 11, 29, 59, 101} ]; // Vincenzo Librandi, Jul 23 2012

QuadPrimes2[5, 0, 6, 10000] (* see A106856 *)

list(lim)=my(v=List([5]),s=[11,29,59,101]); forprime(p=11,lim, if(setsearch(s,p%120), listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Feb 09 2017

The primes are congruent to {5, 11, 29, 59, 101} (mod 120). - T. D. Noe, May 02 2008

A107144 Primes of the form 5x^2 + 8y^2.

Original entry on oeis.org

5, 13, 37, 53, 157, 173, 197, 277, 293, 317, 373, 397, 557, 613, 653, 677, 733, 757, 773, 797, 853, 877, 997, 1013, 1093, 1117, 1213, 1237, 1277, 1373, 1453, 1493, 1597, 1613, 1637, 1693, 1733, 1877, 1933, 1973, 1997, 2053, 2213, 2237, 2293

Offset: 1

T. D. Noe, May 13 2005

Discriminant = -160. See A107132 for more information.

Except for 5, also primes of the form 13x^2 + 8xy + 32y^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. A139827.

[5] cat [ p: p in PrimesUpTo(3000) | p mod 40 in {13, 37} ]; // Vincenzo Librandi, Jul 24 2012

QuadPrimes2[5, 0, 8, 10000] (* see A106856 *)

list(lim)=my(v=List([5]),t); forprime(p=13,lim, t=p%40; if(t==13||t==37, listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Feb 09 2017

Except for 5, the primes are congruent to {13, 37} (mod 40). - T. D. Noe, May 02 2008

A107151 Primes of the form 5x^2 + 9y^2.

Original entry on oeis.org

5, 29, 41, 89, 101, 149, 269, 281, 389, 401, 449, 461, 509, 521, 569, 641, 701, 761, 809, 821, 881, 929, 941, 1049, 1061, 1109, 1181, 1229, 1289, 1301, 1361, 1409, 1481, 1601, 1709, 1721, 1889, 1901, 1949, 2069, 2081, 2129, 2141, 2309, 2381

Offset: 1

T. D. Noe, May 13 2005

Discriminant = -180. See A107132 for more information.

Except for 5, also primes of the form 9x^2 + 6xy + 26y^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. A139827.

[5] cat [ p: p in PrimesUpTo(3000) | p mod 60 in {29, 41 } ]; // Vincenzo Librandi, Jul 24 2012

QuadPrimes2[5, 0, 9, 10000] (* see A106856 *)

list(lim)=my(v=List([5]),t); forprime(p=29,lim, t=p%60; if(t==29||t==41, listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Feb 09 2017

Except for 5, the primes are congruent to {29, 41} (mod 60). - T. D. Noe, May 02 2008

A107167 Primes of the form 5x^2 + 12y^2.

Original entry on oeis.org

5, 17, 53, 113, 137, 173, 197, 233, 257, 293, 317, 353, 557, 593, 617, 653, 677, 773, 797, 857, 953, 977, 1013, 1097, 1193, 1217, 1277, 1373, 1433, 1493, 1553, 1613, 1637, 1697, 1733, 1877, 1913, 1973, 1997, 2153, 2213, 2237, 2273, 2297, 2333

Offset: 1

T. D. Noe, May 13 2005

Discriminant = -240. 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.

[5] cat [p: p in PrimesUpTo(3000) | p mod 60 in [17, 53]]; // Vincenzo Librandi, Jul 25 2012

QuadPrimes2[5, 0, 12, 10000] (* see A106856 *)

list(lim)=my(v=List([5]),t); forprime(p=17,lim, t=p%60; if(t==17||t==53, listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Feb 10 2017

Except for 5, the primes are congruent to {17, 53} (mod 60). - T. D. Noe, May 02 2008

cp's OEIS Frontend

A106889 Primes of the form 2x^2 + 5y^2.

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A107169 Primes of the form 3x^2 + 20y^2.

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A139855 Primes of the form 4x^2+4xy+31y^2.

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A139857 Primes of the form 8x^2 + 15y^2.

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A139858 Primes of the form 8x^2+8xy+17y^2.

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A007639 Primes of form 2n^2 - 2n + 19.

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A107135 Primes of the form 5x^2 + 6y^2.

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A107144 Primes of the form 5x^2 + 8y^2.

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