A102272 -id:A102272 - cp's OEIS frontend

A102269 Primes p such that Q(sqrt(-21p)) has genus characters chi_{-3} = +1, chi_{-7} = +1.

43, 67, 79, 127, 151, 163, 211, 331, 379, 463, 487, 499, 547, 571, 631, 739, 751, 823, 883, 907, 919, 967, 991, 1051, 1087, 1171, 1303, 1327, 1423, 1471, 1579, 1663, 1723, 1747, 1759, 1831, 1999, 2011, 2083, 2143, 2179, 2251, 2311, 2347, 2503, 2647, 2671, 2683, 2731, 2767, 2851, 3019

Offset: 1

N. J. A. Sloane, Feb 19 2005

nonn

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

H. Cohn and J. C. Lagarias, On the existence of fields governing the 2-invariants of the classgroup of Q(sqrt{dp}) as p varies, Math. Comp. 41 (1983), 711-730.

Cf. A102270, A102271, A102272, A102273, A102274, A102275.

[p : p in PrimesUpTo(3000) | p mod 84 in [43, 67, 79]];  // Robin Visser, Mar 13 2024

The primes are congruent to {43, 67, 79} (mod 84). - Robin Visser, Mar 13 2024

More terms from Robin Visser, Mar 13 2024

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

N. J. A. Sloane, Feb 19 2005

nonn

H. Cohn and J. C. Lagarias, On the existence of fields governing the 2-invariants of the classgroup of Q(sqrt{dp}) as p varies, Math. Comp. 41 (1983), 711-730.

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

[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

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

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

N. J. A. Sloane, Feb 19 2005

nonn

H. Cohn and J. C. Lagarias, On the existence of fields governing the 2-invariants of the classgroup of Q(sqrt{dp}) as p varies, Math. Comp. 41 (1983), 711-730.

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

[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

More terms from Robin Visser, Mar 13 2024

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

N. J. A. Sloane Feb 19 2005

nonn

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

H. Cohn and J. C. Lagarias, On the existence of fields governing the 2-invariants of the classgroup of Q(sqrt{dp}) as p varies, Math. Comp. 41 (1983), 711-730.

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

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

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

More terms from Robin Visser, Mar 13 2024

cp's OEIS Frontend

A102269 Primes p such that Q(sqrt(-21p)) has genus characters chi_{-3} = +1, chi_{-7} = +1.

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

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

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Author

Keywords

Links

Crossrefs

Programs

Sage

Extensions

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Formula

Extensions