A045386 - OEIS

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

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OFFSET

1,1

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

MATHEMATICA

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

PROG

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

CROSSREFS

Cf. A002144, A007645, A045373.

Sequence in context: A346497 A185545 A001032 * A084354 A066725 A087340

Adjacent sequences: A045383 A045384 A045385 * A045387 A045388 A045389

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Dec 11 1999

STATUS

approved