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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A106949 Primes of the form 2x^2 + 9y^2.

Original entry on oeis.org

2, 11, 17, 41, 59, 83, 89, 107, 113, 131, 137, 179, 227, 233, 251, 257, 281, 347, 353, 401, 419, 443, 449, 467, 491, 521, 563, 569, 587, 593, 617, 641, 659, 683, 761, 809, 827, 857, 881, 929, 947, 953, 971, 977, 1019, 1049, 1091, 1097, 1163, 1187, 1193
Offset: 1

Views

Author

T. D. Noe, May 09 2005

Keywords

Comments

Discriminant = -72.

Links

Programs

  • Magma
    [ p: p in PrimesUpTo(2000) | p mod 24 in {2, 11, 17} ]; // Vincenzo Librandi, Jul 22 2012
  • Mathematica
    QuadPrimes2[2, 0, 9, 10000] (* see A106856 *)
  • PARI
    {a(n)= my(m, c); if(n<1, 0, c=0; m=0; while( cMichael Somos, Aug 19 2006 */
  • PARI
    list(lim)=my(v=List([2]),t); forprime(p=11,lim, t=p%24; if(t==11||t==17, listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Feb 09 2017

Formula

Primes congruent to 2,11,17 modulo 24. - Michael Somos, Aug 19 2006

A106989 Primes of the form x^2-xy+23y^2, with x and y nonnegative.

Original entry on oeis.org

23, 29, 43, 53, 79, 107, 113, 127, 179, 191, 211, 233, 263, 277, 337, 347, 373, 389, 443, 491, 547, 569, 571, 599, 641, 653, 659, 673, 701, 751, 757, 809, 823, 883, 907, 911, 919, 953, 991, 1031, 1093, 1117, 1171, 1187, 1213, 1283, 1297, 1303, 1327
Offset: 1

Views

Author

T. D. Noe, May 09 2005

Keywords

Comments

Discriminant=-91.
Also, primes that are squares (mod 91), or equivalently, with Legendre symbols (p|7) = (p|13) = 1. Included as subsequence in A191054 which are primes with Jacobi symbol (p|7*13) = 1, including also primes with (p|7) = (p|13) = -1. - David Broadhurst and M. F. Hasler, Jan 15 2016

Links

Programs

  • Mathematica
    QuadPrimes2[1, -1, 23, 10000] (* see A106856 *)
  • PARI
    is(p)=issquare(Mod(p,91))&&isprime(p) \\ M. F. Hasler, Jan 15 2016

A107013 Primes of the form x^2-xy+25y^2, with x and y nonnegative.

Original entry on oeis.org

31, 37, 67, 97, 103, 157, 163, 181, 199, 223, 229, 313, 331, 367, 379, 397, 421, 433, 463, 487, 499, 577, 619, 631, 643, 661, 691, 709, 727, 751, 757, 823, 829, 859, 883, 907, 991, 1021, 1039, 1087, 1093, 1123, 1153, 1171, 1213, 1237, 1279, 1291, 1303
Offset: 1

Views

Author

T. D. Noe, May 09 2005

Keywords

Comments

Discriminant=-99.

Links

Programs

  • Mathematica
    QuadPrimes2[1, -1, 25, 10000] (* see A106856 *)

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

Views

Author

T. D. Noe, May 13 2005

Keywords

Comments

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

Links

Crossrefs

Cf. A139827.

Programs

  • Magma
    [ p: p in PrimesUpTo(3000) | p mod 120 in {5, 11, 29, 59, 101} ]; // Vincenzo Librandi, Jul 23 2012
  • Mathematica
    QuadPrimes2[5, 0, 6, 10000] (* see A106856 *)
  • PARI
    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

Formula

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

A107141 Primes of the form 4x^2 + 9y^2.

Original entry on oeis.org

13, 73, 97, 109, 181, 229, 241, 277, 337, 409, 421, 457, 541, 709, 733, 757, 829, 1009, 1033, 1093, 1117, 1129, 1153, 1213, 1237, 1249, 1381, 1453, 1489, 1597, 1609, 1621, 1669, 1753, 1777, 1873, 2017, 2029, 2089, 2113, 2161, 2221, 2281
Offset: 1

Views

Author

T. D. Noe, May 13 2005

Keywords

Comments

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 "negative character". - N. J. A. Sloane, Jul 30 2015

References

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

Links

Programs

  • Mathematica
    QuadPrimes2[4, 0, 9, 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)\9), if(isprime(t=w+9*y^2), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 09 2017

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

Views

Author

T. D. Noe, May 13 2005

Keywords

Comments

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

Links

Crossrefs

Cf. A139827.

Programs

  • Magma
    [5] cat [ p: p in PrimesUpTo(3000) | p mod 40 in {13, 37} ]; // Vincenzo Librandi, Jul 24 2012
  • Mathematica
    QuadPrimes2[5, 0, 8, 10000] (* see A106856 *)
  • PARI
    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

Formula

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

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

A107159 Primes of the form 4x^2 + 13y^2.

Original entry on oeis.org

13, 17, 29, 113, 157, 181, 269, 313, 337, 373, 389, 521, 601, 641, 653, 673, 701, 797, 809, 1069, 1109, 1117, 1153, 1213, 1249, 1453, 1481, 1609, 1613, 1621, 1637, 1777, 1933, 1949, 1973, 2053, 2081, 2089, 2129, 2213, 2237, 2297, 2341, 2357, 2393
Offset: 1

Views

Author

T. D. Noe, May 13 2005

Keywords

Comments

Discriminant = -208. See A107132 for more information.

Links

Programs

  • Mathematica
    QuadPrimes2[4, 0, 13, 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)\13), if(isprime(t=w+13*y^2), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 09 2017

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
Previous Showing 61-70 of 574 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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