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.

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A107161 Primes of the form 2x^2 + 27y^2.

Original entry on oeis.org

2, 29, 59, 227, 251, 269, 293, 419, 443, 677, 683, 773, 821, 827, 1013, 1187, 1277, 1301, 1373, 1451, 1493, 1523, 1709, 1733, 1811, 1901, 1949, 2027, 2237, 2243, 2339, 2357, 2381, 2477, 2579, 2693, 2699, 2909, 3299, 3371, 3389, 3413, 3467
Offset: 1

Views

Author

T. D. Noe, May 13 2005

Keywords

Comments

Discriminant = -216. See A107132 for more information.

Links

Programs

  • Mathematica
    QuadPrimes2[2, 0, 27, 10000] (* see A106856 *)
With[{nn=50},Take[Union[Select[2#[[1]]+27#[[2]]&/@(Tuples[Range[ 0,nn],2]^2),PrimeQ]],nn]] (* Harvey P. Dale, Jun 15 2014 *)
  • PARI
    list(lim)=my(v=List(),w,t); for(x=1, sqrtint(lim\2), w=2*x^2; for(y=0, sqrtint((lim-w)\27), if(isprime(t=w+27*y^2), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 09 2017

Extensions

Terms, including b-file, checked by Harvey P. Dale, Jun 16 2014

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

Views

Author

T. D. Noe, May 13 2005

Keywords

Comments

Discriminant = -240. See A107132 for more information.

Links

Crossrefs

Cf. A139827.

Programs

  • Magma
    [5] cat [p: p in PrimesUpTo(3000) | p mod 60 in [17, 53]]; // Vincenzo Librandi, Jul 25 2012
  • Mathematica
    QuadPrimes2[5, 0, 12, 10000] (* see A106856 *)
  • PARI
    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

Formula

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

A107218 Primes of the form 4x^2 + 25y^2.

Original entry on oeis.org

29, 41, 61, 89, 229, 241, 281, 349, 421, 509, 601, 641, 661, 701, 709, 769, 809, 821, 881, 1009, 1049, 1109, 1181, 1201, 1229, 1249, 1289, 1301, 1321, 1381, 1409, 1481, 1549, 1669, 1709, 1789, 1801, 1901, 2029, 2069, 2089, 2141, 2161, 2221, 2281
Offset: 1

Views

Author

T. D. Noe, May 13 2005

Keywords

Comments

Discriminant = -400. See A107132 for more information.

Links

Programs

  • Mathematica
    QuadPrimes2[4, 0, 25, 10000] (* see A106856 *)
  • PARI
    list(lim)=my(v=List(),w,t); for(x=1, sqrtint(lim\4), w=4*x^2; for(y=1, sqrtint((lim-w)\25), if(isprime(t=w+25*y^2), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 10 2017

A107219 Primes of the form x^2 + 100y^2.

Original entry on oeis.org

101, 109, 149, 181, 269, 389, 401, 409, 449, 461, 521, 541, 569, 761, 829, 929, 941, 1021, 1061, 1069, 1129, 1361, 1429, 1489, 1601, 1609, 1621, 1721, 1741, 1861, 1889, 1949, 2081, 2129, 2269, 2309, 2441, 2549, 2609, 2621, 2689, 2749, 2789
Offset: 1

Views

Author

T. D. Noe, May 13 2005

Keywords

Comments

Discriminant = -400. See A107132 for more information.

Links

Programs

  • Mathematica
    QuadPrimes2[1, 0, 100, 10000] (* see A106856 *)
  • PARI
    list(lim)=my(v=List(),w,t); for(x=1, sqrtint(lim\1), w=x^2; for(y=1, sqrtint((lim-w)\100), if(isprime(t=w+100*y^2), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 10 2017

A107133 Primes of the form 4x^2 + 7y^2.

Original entry on oeis.org

7, 11, 23, 43, 67, 71, 79, 107, 127, 151, 163, 179, 191, 211, 239, 263, 331, 347, 359, 379, 431, 443, 463, 487, 491, 499, 547, 571, 599, 631, 659, 683, 739, 743, 751, 823, 827, 863, 883, 907, 911, 919, 947, 967, 991, 1019, 1031, 1051, 1087, 1103, 1163
Offset: 1

Views

Author

T. D. Noe, May 13 2005

Keywords

Comments

Discriminant = -112. See A107132 for more information.

Links

Crossrefs

Cf. A139827.

Programs

  • Mathematica
    QuadPrimes2[4, 0, 7, 10000] (* see A106856 *)
  • PARI
    list(lim)=my(v=List(),w,t); for(x=0, sqrtint(lim\4), w=4*x^2; for(y=1, sqrtint((lim-w)\7), if(isprime(t=w+7*y^2), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 09 2017

Formula

Except for 7, the primes are congruent to {11, 15, 23} (mod 28). - T. D. Noe, May 02 2008

A107134 Primes of the form x^2+28y^2.

Original entry on oeis.org

29, 37, 53, 109, 113, 137, 149, 193, 197, 233, 277, 281, 317, 337, 373, 389, 401, 421, 449, 457, 541, 557, 569, 613, 617, 641, 653, 673, 701, 709, 757, 809, 821, 877, 953, 977, 1009, 1033, 1061, 1093, 1117, 1129, 1201, 1213, 1229, 1289, 1297, 1373, 1381
Offset: 1

Views

Author

T. D. Noe, May 13 2005

Keywords

Comments

Discriminant=-112. See A107132 for more information.

Links

Crossrefs

Cf. A139643.

Programs

  • Magma
    [ p: p in PrimesUpTo(2000) | p mod 28 in {1, 9, 25} ]; // Vincenzo Librandi, Jul 23 2012
  • Mathematica
    QuadPrimes2[1, 0, 28, 10000] (* see A106856 *)

Formula

The primes are congruent to {1, 9, 25} (mod 28). - T. D. Noe, Apr 29 2008

A107137 Primes of the form 2x^2 + 15y^2.

Original entry on oeis.org

2, 17, 23, 47, 113, 137, 167, 233, 257, 263, 353, 383, 503, 593, 617, 647, 743, 857, 863, 887, 953, 977, 983, 1097, 1103, 1193, 1217, 1223, 1367, 1433, 1487, 1553, 1583, 1607, 1697, 1823, 1847, 1913, 2063, 2087, 2153, 2207, 2273, 2297, 2393
Offset: 1

Views

Author

T. D. Noe, May 13 2005

Keywords

Comments

Discriminant = -120. See A107132 for more information.

Links

Crossrefs

Cf. A139827.

Programs

  • Magma
    [ p: p in PrimesUpTo(3000) | p mod 120 in {2, 17, 23, 47, 113} ]; // Vincenzo Librandi, Jul 24 2012
  • Mathematica
    QuadPrimes2[2, 0, 15, 10000] (* see A106856 *)
  • PARI
    list(lim)=my(v=List([2]), s=[17, 23, 47, 113]); forprime(p=11, lim, if(setsearch(s, p%120), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Feb 09 2017

Formula

The primes are congruent to {2, 17, 23, 47, 113} (mod 120). - T. D. Noe, May 02 2008

A107138 Primes of the form 3x^2 + 11y^2.

Original entry on oeis.org

3, 11, 23, 47, 59, 71, 179, 191, 251, 311, 383, 419, 443, 467, 587, 599, 647, 683, 719, 839, 863, 911, 947, 971, 983, 1103, 1259, 1307, 1367, 1439, 1499, 1511, 1523, 1571, 1607, 1787, 1871, 1907, 2003, 2027, 2039, 2099, 2267, 2399, 2423, 2447, 2531
Offset: 1

Views

Author

T. D. Noe, May 13 2005

Keywords

Comments

Discriminant = -132. See A107132 for more information.

Links

Crossrefs

Cf. A139827.

Programs

  • Magma
    [ p: p in PrimesUpTo(3000) | p mod 132 in {3, 11, 23, 47, 59, 71, 119} ]; // Vincenzo Librandi, Jul 24 2012
  • Mathematica
    QuadPrimes2[3, 0, 11, 10000] (* see A106856 *)
  • PARI
    list(lim)=my(v=List([3]), s=[11, 23, 47, 59, 71, 119]); forprime(p=11, lim, if(setsearch(s, p%132), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Feb 09 2017

Formula

The primes are congruent to {3, 11, 23, 47, 59, 71, 119} (mod 132). - T. D. Noe, May 02 2008

A107139 Primes of the form 2x^2 + 17y^2.

Original entry on oeis.org

2, 17, 19, 67, 89, 179, 251, 281, 353, 409, 433, 443, 457, 467, 491, 523, 587, 739, 883, 937, 953, 1033, 1171, 1283, 1307, 1409, 1427, 1481, 1483, 1619, 1699, 1721, 1777, 1801, 1889, 1993, 2083, 2089, 2099, 2129, 2347, 2467, 2473, 2609, 2633
Offset: 1

Views

Author

T. D. Noe, May 13 2005

Keywords

Comments

Discriminant = -136. See A107132 for more information.

Links

Programs

  • Mathematica
    QuadPrimes2[2, 0, 17, 10000] (* see A106856 *)
  • PARI
    list(lim)=my(v=List(),w,t); for(x=0, sqrtint(lim\2), w=2*x^2; for(y=0, sqrtint((lim-w)\17), if(isprime(t=w+17*y^2), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 09 2017

A107140 Primes of the form 5x^2 + 7y^2.

Original entry on oeis.org

5, 7, 73, 83, 157, 257, 383, 433, 523, 563, 587, 647, 727, 853, 857, 887, 1013, 1063, 1097, 1153, 1237, 1567, 1613, 1627, 1697, 1777, 1847, 2063, 2203, 2273, 2393, 2467, 2707, 2803, 2887, 2897, 2917, 3167, 3407, 3433, 3643, 3673, 3727, 3793
Offset: 1

Views

Author

T. D. Noe, May 13 2005

Keywords

Comments

Discriminant = -140. See A107132 for more information.

Links

Programs

  • Mathematica
    QuadPrimes2[5, 0, 7, 10000] (* see A106856 *)
  • PARI
    list(lim)=my(v=List(),w,t); for(x=0, sqrtint(lim\5), w=5*x^2; for(y=0, sqrtint((lim-w)\7), if(isprime(t=w+7*y^2), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 09 2017
Previous Showing 11-20 of 87 results. Next

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