cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 21-30 of 68 results. Next

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

Views

Author

T. D. Noe, May 13 2005

Keywords

Comments

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

Links

Crossrefs

Cf. A139827.

Programs

  • Magma
    [5] cat [ p: p in PrimesUpTo(3000) | p mod 60 in {29, 41 } ]; // Vincenzo Librandi, Jul 24 2012
  • Mathematica
    QuadPrimes2[5, 0, 9, 10000] (* see A106856 *)
  • PARI
    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

Formula

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

A139831 Primes of the form 2x^2+2xy+23y^2.

Original entry on oeis.org

2, 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

Views

Author

T. D. Noe, May 02 2008

Keywords

Comments

Discriminant=-180. See A139827 for more information.
Except for 2, also primes of the forms 3x^2+20y^2 (A107169) and 8x^2+4xy+23y^2. See A140633. - T. D. Noe, May 19 2008

Links

Programs

  • Magma
    [2] cat[ p: p in PrimesUpTo(3000) | p mod 60 in {23, 47}]; // Vincenzo Librandi, Jul 29 2012
  • Mathematica
    QuadPrimes2[2, -2, 23, 10000] (* see A106856 *)

Formula

Except for 2, the primes are congruent to {23, 47} (mod 60).

A139850 Primes of the form 11x^2 + 8xy + 11y^2.

Original entry on oeis.org

11, 71, 179, 191, 239, 359, 431, 491, 599, 659, 911, 1019, 1031, 1439, 1451, 1499, 1619, 1871, 2039, 2111, 2339, 2459, 2531, 2591, 2699, 2711, 2879, 3011, 3119, 3299, 3371, 3539, 3719, 3851, 4019, 4139, 4211, 4271, 4391, 4691, 4799, 5051
Offset: 1

Views

Author

T. D. Noe, May 02 2008

Keywords

Comments

Discriminant = -420. See A139827 for more information.
Also primes of the forms 11x^2 + 6xy + 39y^2 and 11x^2 + 10xy + 50y^2. See A140633. - T. D. Noe, May 19 2008

Links

Programs

  • Magma
    [ p: p in PrimesUpTo(6000) | p mod 420 in {11, 71, 179, 191, 239, 359}]; // Vincenzo Librandi, Jul 29 2012
  • Mathematica
    Union[QuadPrimes2[11, 8, 11, 10000], QuadPrimes2[11, -8, 11, 10000]] (* see A106856 *)
  • PARI
    list(lim)=my(v=List(), s=[11, 71, 179, 191, 239, 359]); forprime(p=11, lim, if(setsearch(s, p%420), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Feb 10 2017

Formula

The primes are congruent to {11, 71, 179, 191, 239, 359} (mod 420).

A139854 Primes of the form 3x^2 + 40y^2.

Original entry on oeis.org

3, 43, 67, 163, 283, 307, 523, 547, 643, 787, 883, 907, 1123, 1483, 1627, 1723, 1747, 1867, 1987, 2083, 2203, 2347, 2467, 2683, 2707, 2803, 3067, 3163, 3187, 3307, 3547, 3643, 3907, 4003, 4027, 4243, 4363, 4483, 4507, 4603, 4723, 4987, 5107
Offset: 1

Views

Author

T. D. Noe, May 02 2008

Keywords

Comments

Discriminant=-480. See A139827 for more information.
Except for 3, also primes of the form 27x^2+12xy+28y^2. See A140633. - T. D. Noe, May 19 2008

Links

Crossrefs

Cf. A140633.

Programs

  • Magma
    [3] cat [ p: p in PrimesUpTo(6000) | p mod 120 in {43, 67}]; // Vincenzo Librandi, Jul 29 2012
  • Mathematica
    QuadPrimes2[3, 0, 40, 10000] (* see A106856 *)
  • PARI
    list(lim)=my(v=List(),w,t); for(x=1, sqrtint(lim\3), w=3*x^2; for(y=0, sqrtint((lim-w)\40), if(isprime(t=w+40*y^2), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 22 2017

Formula

Except for 3, the primes are congruent to {43, 67} (mod 120).

A139860 Primes of the form 12x^2+12xy+13y^2.

Original entry on oeis.org

13, 37, 157, 277, 373, 397, 613, 733, 757, 853, 877, 997, 1093, 1117, 1213, 1237, 1453, 1597, 1693, 1933, 2053, 2293, 2437, 2557, 2677, 2797, 2917, 3037, 3253, 3373, 3517, 3613, 3637, 3733, 3853, 3877, 4093, 4357, 4597, 4813, 4933, 4957
Offset: 1

Views

Author

T. D. Noe, May 02 2008

Keywords

Comments

Discriminant=-480. See A139827 for more information.
Also primes of the forms 13x^2+2xy+37y^2 and 13x^2+4xy+28y^2. See A140633. - T. D. Noe, May 19 2008

Links

Programs

  • Magma
    [ p: p in PrimesUpTo(6000) | p mod 120 in {13, 37}]; // Vincenzo Librandi, Jul 29 2012
  • Mathematica
    QuadPrimes2[12, -12, 13, 10000] (* see A106856 *)

Formula

The primes are congruent to {13, 37} (mod 120).

Extensions

Corrected and extended b-file - Ray Chandler, Jul 30 2014

A139874 Primes of the form 3x^2 + 56y^2.

Original entry on oeis.org

3, 59, 83, 131, 227, 251, 419, 467, 563, 587, 971, 1091, 1259, 1307, 1427, 1571, 1811, 1907, 1931, 1979, 2099, 2243, 2267, 2411, 2579, 2819, 2939, 3083, 3251, 3323, 3491, 3659, 3779, 3923, 3947, 4091, 4259, 4283, 4451, 4787, 4931, 5003
Offset: 1

Views

Author

T. D. Noe, May 02 2008

Keywords

Comments

Discriminant = -672. See A139827 for more information.
Except for 3, also primes of the form 20x^2 + 12xy + 27y^2. See A140633. - T. D. Noe, May 19 2008

Links

Programs

  • Magma
    [3] cat [ p: p in PrimesUpTo(6000) | p mod 168 in {59, 83, 131}]; // Vincenzo Librandi, Jul 30 2012
  • Mathematica
    QuadPrimes2[3, 0, 56, 10000] (* see A106856 *)
  • PARI
    list(lim)=my(v=List(),w,t); for(x=1, sqrtint(lim\3), w=3*x^2; for(y=0, sqrtint((lim-w)\56), if(isprime(t=w+56*y^2), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Mar 07 2017

Formula

Except for 3, the primes are congruent to {59, 83, 131} (mod 168).

A139880 Primes of the form 13x^2+2xy+13y^2.

Original entry on oeis.org

13, 61, 157, 181, 229, 349, 397, 661, 733, 829, 853, 997, 1021, 1069, 1237, 1669, 1693, 1741, 1861, 2029, 2341, 2677, 2749, 2917, 3037, 3181, 3253, 3373, 3517, 3541, 3709, 3853, 3877, 4021, 4093, 4261, 4357, 4549, 4597, 4861, 4933, 5101
Offset: 1

Views

Author

T. D. Noe, May 02 2008

Keywords

Comments

Discriminant=-672. See A139827 for more information.
Also primes of the forms 13x^2+4xy+52y^2 and 13x^2+8xy+40y^2. See A140633. - T. D. Noe, May 19 2008

Links

Programs

  • Magma
    [ p: p in PrimesUpTo(6000) | p mod 168 in {13, 61, 157}]; // Vincenzo Librandi, Jul 30 2012
  • Mathematica
    Union[QuadPrimes2[13, 2, 13, 10000], QuadPrimes2[13, -2, 13, 10000]] (* see A106856 *)

Formula

The primes are congruent to {13, 61, 157} (mod 168).

A139897 Primes of the form 3*x^2+80*y^2.

Original entry on oeis.org

3, 83, 107, 227, 347, 443, 467, 563, 587, 683, 827, 947, 1163, 1187, 1283, 1307, 1427, 1523, 1667, 1787, 1907, 2003, 2027, 2243, 2267, 2843, 2963, 3083, 3203, 3323, 3347, 3467, 3803, 3923, 3947, 4283, 4523, 4547, 4643, 4787, 5003, 5147
Offset: 1

Views

Author

T. D. Noe, May 02 2008

Keywords

Comments

Discriminant=-960. See A139827 for more information.
Except for 3, also primes of the form 27*x^2+24*x*y+32*y^2. See A140633. - T. D. Noe, May 19 2008
Excepting for the first term, 3, the members of this sequence seem to be terms of A123239 which are prime in k(i), k(rho) & k(sqrt(5)). [From A.K. Devaraj, Nov 30 2009]

Links

Programs

  • Magma
    [3] cat [p: p in PrimesUpTo(6000) | p mod 120 in [83, 107]]; // Vincenzo Librandi, Jul 31 2012
  • Mathematica
    QuadPrimes2[3, 0, 80, 10000] (* see A106856 *)

Formula

Except for 3, primes congruent to 83 or 107 (mod 120).

A139998 Primes of the form 31x^2+22xy+31y^2.

Original entry on oeis.org

31, 199, 271, 439, 1039, 1231, 1279, 1399, 1879, 1951, 2239, 2551, 2719, 2791, 3079, 3391, 3559, 3631, 3919, 4231, 4591, 4639, 4759, 5431, 5479, 6079, 6151, 6271, 6991, 7159, 7591, 7759, 7951, 8431, 8599, 8839, 9439, 9511, 9631, 9679
Offset: 1

Views

Author

T. D. Noe, May 02 2008

Keywords

Comments

Discriminant=-3360. See A139827 for more information.
Also primes of the forms 31x^2+18xy+111y^2 and 31x^2+10xy+55y^2. See A140633. - T. D. Noe, May 19 2008

Links

Programs

  • Magma
    [p: p in PrimesUpTo(12000) | p mod 840 in [31, 199, 271, 391, 439, 559]]; // Vincenzo Librandi, Aug 03 2012
  • Mathematica
    Union[QuadPrimes2[31, 22, 31, 10000], QuadPrimes2[31, -22, 31, 10000]] (* see A106856 *)

Formula

The primes are congruent to {31, 199, 271, 391, 439, 559} (mod 840).

A140013 Primes of the form 41x^2+38xy+41y^2.

Original entry on oeis.org

41, 281, 569, 761, 809, 1289, 1361, 1481, 1601, 1889, 2081, 2129, 2441, 2609, 2801, 2969, 3209, 3329, 3449, 3761, 3929, 4001, 4241, 4289, 4649, 4721, 5081, 5441, 5849, 6089, 6569, 6761, 8081, 8609, 8681, 9041, 9209, 9281, 9521, 9929, 10529
Offset: 1

Views

Author

T. D. Noe, May 02 2008

Keywords

Comments

Discriminant=-5280. See A139827 for more information.
Also primes of the forms 41x^2+6xy+129y^2 and 41x^2+10xy+65y^2. See A140633. - T. D. Noe, May 19 2008

Links

Programs

  • Magma
    [ p: p in PrimesUpTo(11000) | p mod 1320 in {41, 161, 281, 329, 569, 689, 761, 809, 1121, 1289} ]; // _Vincenzo Librandi-, Aug 05 2012
  • Mathematica
    Union[QuadPrimes2[41, 38, 41, 10000], QuadPrimes2[41, -38, 41, 10000]] (* see A106856 *)

Formula

The primes are congruent to {41, 161, 281, 329, 569, 689, 761, 809, 1121, 1289} (mod 1320).
Previous Showing 21-30 of 68 results. Next

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