A045386 Primes congruent to {1, 2, 4} mod 7.

2, 11, 23, 29, 37, 43, 53, 67, 71, 79, 107, 109, 113, 127, 137, 149, 151, 163, 179, 191, 193, 197, 211, 233, 239, 263, 277, 281, 317, 331, 337, 347, 359, 373, 379, 389, 401, 421, 431, 443, 449, 457, 463, 487, 491, 499, 541, 547, 557, 569, 571, 599, 613, 617, 631, 641, 653, 659, 673

Offset: 1

Author

N. J. A. Sloane, Dec 11 1999

Keywords

• nonn
• easy

Comments

Rational primes that decompose in the field Q(sqrt(-7)). - N. J. A. Sloane, Dec 25 2017

All these primes can be represented by the binary quadratic form x^2 + xy + 2y^2. - Alonso del Arte, Jun 13 2014. Indeed, apart from the fact that 7 is missing, this appears to coincide with A045373. - N. J. A. Sloane, Jun 14 2014

References

• Şaban Alaca & Kenneth S. Williams, Introductory Algebraic Number Theory. Cambridge: Cambridge University Press (2004) p. 48, Theorem 2.5.4.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)
• Index to sequences related to decomposition of primes in quadratic fields

Crossrefs

Cf. A002144, A007645, A045373.

Programs

Magma

[p: p in PrimesUpTo(600) | p mod 7 in [1, 2, 4]]; // Vincenzo Librandi, Aug 11 2012

Mathematica

Select[Prime[Range[300]], MemberQ[{1, 2, 4}, Mod[#, 7]] &] (* Vincenzo Librandi, Aug 11 2012 *)