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A033207 Primes of form x^2+7*y^2. 7
7, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Except for a(1) = 7, these are the primes which can be written in the form a^2 + 7*b^2 with a > 0 and b > 0. - V. Raman, Sep 08 2012

These are the primes p for which p^3 - 1 is divisible by 7.  There are two exceptions: p = 2 is not in the sequence even though 2^3 - 1 is divisible by 7, and p = 7 is in the sequence even though 7^3 - 1 is not divisible by 7.  Except for p = 7, if p^3 - 1 is not divisible by 7, it is congruent to 5 (mod 7). - Richard R. Forberg, Jun 03 2013

REFERENCES

David A. Cox, "Primes of the Form x^2 + n y^2", Wiley, 1989.

LINKS

T. D. Noe and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from T. D. Noe]

Sushma Palimar and B. R. Shankar, Mersenne Primes in Real Quadratic Fields, Journal of Integer Sequences, Vol. 15 (2012), #12.5.6.

N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

FORMULA

Primes congruent to {1, 7, 9, 11, 15, 23, 25} (mod 28). - T. D. Noe, Apr 29 2008

MATHEMATICA

QuadPrimes2[1, 0, 7, 10000] (* see A106856 *)

PROG

(PARI) is(n)=kronecker(n, 7)>=0 && isprime(n) && n>2 \\ Charles R Greathouse IV, Nov 19 2012

CROSSREFS

Essentially the same as A045373. Primes in A020670.

Cf. A002344, A002345, A139643.

Sequence in context: A211433 A039511 A103667 * A095084 A182569 A067790

Adjacent sequences:  A033204 A033205 A033206 * A033208 A033209 A033210

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified July 15 14:07 EDT 2019. Contains 325030 sequences. (Running on oeis4.)