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.

Showing 1-6 of 6 results.

A102270 2-class number of Q(sqrt(-21p)) as p runs through primes in A102269.

Original entry on oeis.org

16, 8, 8, 8, 16, 8, 16, 16, 16, 8, 16, 32, 8, 8, 8, 8, 32, 8, 16, 64, 32, 8, 32, 8, 8, 128, 32, 32, 32, 16, 8, 8, 8, 16, 16, 8, 8, 8, 128, 16, 8, 8, 16, 32, 8, 16, 32, 8, 8, 8, 128, 8, 8, 8, 16, 8, 64, 8, 8, 8, 16, 8, 16, 16, 16, 8, 8, 16, 32, 16, 8, 8, 8, 64, 32, 64, 16, 64, 8, 16, 32
Offset: 1

Views

Author

N. J. A. Sloane, Feb 19 2005

Keywords

Links

Crossrefs

Cf. A102269, A102271, A102272, A102273, A102274, A102275.

Programs

  • Sage
    [2^QuadraticField(-21*p).class_number().valuation(2) for p in Primes()[:1000] if (p%84) in [43, 67, 79]] # Robin Visser, Mar 13 2024

Extensions

More terms from Robin Visser, Mar 13 2024

A102273 Primes p such that Q(sqrt(-21p)) has genus characters chi_{-3} = -1, chi_{-7} = +1.

Original entry on oeis.org

11, 23, 71, 107, 179, 191, 239, 263, 347, 359, 431, 443, 491, 599, 659, 683, 743, 827, 863, 911, 947, 1019, 1031, 1103, 1163, 1187, 1283, 1367, 1439, 1451, 1499, 1523, 1583, 1607, 1619, 1667, 1787, 1871, 2003, 2027, 2039, 2087
Offset: 1

Views

Author

N. J. A. Sloane, Feb 19 2005

Keywords

Comments

The 2-class number of these fields is always 4.
Primes of the form 2x^2 - 2xy + 11y^2 with x nonnegative and y positive. - T. D. Noe, May 08 2005
Also primes of the forms 8x^2 + 4xy + 11y^2 and 11x^2 + 2xy + 23y^2. See A140633. - T. D. Noe, May 19 2008
The discriminant of positive definite binary quadratic form (2,2,11) is -84. - Hugo Pfoertner, Jul 14 2019

Links

Crossrefs

Cf. A102269-A102275.
Cf. A139827.

Programs

  • Magma
    [p: p in PrimesUpTo(3000) | p mod 84 in [2, 11, 23, 71]]; // Vincenzo Librandi, Jul 19 2012
  • Mathematica
    f[x_,y_]:=2*x^2+2*x*y+11*y^2; lst={};Do[Do[p=f[x,y];If[PrimeQ[p],AppendTo[lst,p]],{y,-5!,6!}],{x,-5!,6!}];Take[Union[lst],5! ] (* Vladimir Joseph Stephan Orlovsky, Jul 06 2009 *)

Formula

The primes are congruent to {2, 11, 23, 71} (mod 84). - T. D. Noe, May 02 2008

A102271 Primes of the form 3*x^2 + 7*y^2.

Original entry on oeis.org

3, 7, 19, 31, 103, 139, 199, 223, 271, 283, 307, 367, 439, 523, 607, 619, 643, 691, 727, 787, 811, 859, 1039, 1063, 1123, 1231, 1279, 1291, 1399, 1447, 1459, 1483, 1531, 1543, 1567, 1627, 1699, 1783, 1867, 1879, 1951, 1987, 2131, 2203, 2239, 2287, 2371, 2383
Offset: 1

Views

Author

N. J. A. Sloane, Feb 19 2005

Keywords

Comments

Primes p such that Q(sqrt(-21p)) has genus characters chi_{-3} = +1, chi_{-7} = -1.

Links

Crossrefs

Cf. A102269-A102275, A139827.

Programs

  • Magma
    [p: p in PrimesUpTo(3000) | p mod 84 in [3, 7, 19, 31, 55]]; // Vincenzo Librandi, Jul 19 2012
  • Mathematica
    m=3; n=7; pLst={}; lim=3000; xMax=Sqrt[lim/m]; yMax=Sqrt[lim/n]; Do[p=m*x^2+n*y^2; If[pT. D. Noe, May 05 2005 *)
QuadPrimes2[3, 0, 7, 10000] (* see A106856 *)
  • PARI
    list(lim)=my(v=List(),w,t); for(x=0, sqrtint(lim\3), w=3*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

Formula

The primes are congruent to {3, 7, 19, 31, 55} (mod 84). - T. D. Noe, May 02 2008

A102275 2-class number of Q(sqrt(-21p)) as p runs through primes in A102274.

Original entry on oeis.org

8, 32, 8, 8, 8, 32, 64, 8, 16, 16, 64, 8, 16, 16, 16, 8, 32, 8, 8, 8, 32, 8, 16, 8, 8, 8, 8, 8, 32, 16, 8, 16, 128, 32, 32, 8, 32, 16, 32, 8, 128, 16, 16, 16, 8, 8, 16, 8, 16, 8, 8, 8, 16, 16, 16, 8, 64, 8, 8, 16, 8, 8, 8, 8, 8, 8, 8, 16, 16, 16, 32, 16, 8, 16, 32, 16, 8, 8, 32, 16, 16
Offset: 1

Views

Author

N. J. A. Sloane, Feb 19 2005

Keywords

Links

Crossrefs

Cf. A102269, A102270, A102271, A102272, A102273, A102274.

Programs

  • Sage
    [2^QuadraticField(-21*p).class_number().valuation(2) for p in Primes()[:1000] if (p%84) in [47, 59, 83]] # Robin Visser, Mar 13 2024

Extensions

a(19) corrected and more terms from Robin Visser, Mar 13 2024

A102272 2-class number of Q(sqrt(-21p)) as p runs through primes in A102271.

Original entry on oeis.org

16, 8, 8, 8, 16, 16, 8, 32, 16, 16, 16, 8, 16, 8, 64, 8, 8, 8, 8, 128, 16, 8, 8, 32
Offset: 1

Views

Author

N. J. A. Sloane, Feb 19 2005

Keywords

Links

Crossrefs

Cf. A102269, A102270, A102271, A102273, A102274, A102275.

A102274 Primes p such that Q(sqrt(-21p)) has genus characters chi_{-3} = -1, chi_{-7} = -1.

Original entry on oeis.org

47, 59, 83, 131, 167, 227, 251, 311, 383, 419, 467, 479, 503, 563, 587, 647, 719, 839, 887, 971, 983, 1091, 1151, 1223, 1259, 1307, 1319, 1427, 1487, 1511, 1559, 1571, 1811, 1823, 1847, 1907, 1931, 1979, 2063, 2099, 2243, 2267, 2351, 2399, 2411, 2579, 2663, 2687, 2819, 2903, 2939, 2999
Offset: 1

Views

Author

N. J. A. Sloane Feb 19 2005

Keywords

Comments

Primes p such that p is 3 (mod 4) and (-3/p) = (-7/p) = -1, where (k/n) is the Kronecker symbol. - Robin Visser, Mar 13 2024

Links

Crossrefs

Cf. A102269, A102270, A102271, A102272, A102273, A102275.

Programs

  • Magma
    [p : p in PrimesUpTo(3000) | p mod 84 in [47, 59, 83]];  // Robin Visser, Mar 13 2024

Formula

The primes are congruent to {47, 59, 83} (mod 84). - Robin Visser, Mar 13 2024

Extensions

More terms from Robin Visser, Mar 13 2024
Showing 1-6 of 6 results.

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