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A038872 Primes congruent to {0, 1, 4} mod 5. 72
5, 11, 19, 29, 31, 41, 59, 61, 71, 79, 89, 101, 109, 131, 139, 149, 151, 179, 181, 191, 199, 211, 229, 239, 241, 251, 269, 271, 281, 311, 331, 349, 359, 379, 389, 401, 409, 419, 421, 431, 439, 449, 461, 479, 491, 499, 509, 521, 541, 569, 571, 599, 601, 619 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also odd primes p such that 5 is a square mod p: (5/p) = +1.

Primes of the form x^2+x*y-y^2 (as well as of the form x^2+3*x*y+y^2), both with discriminant = 5 and class number = 1. Binary quadratic forms a*x^2+b*x*y+c*y^2 have discriminant d=b^2-4ac and gcd(a,b,c)=1. [This was originally a separate entry, submitted by Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales, Jun 06 2008. R. J. Mathar proved on Jul 22 2008 that this coincides with the present sequence.]

Also primes of the form 5x^2-y^2 (cf. A031363). - N. J. A. Sloane, May 30 2014

Is this the same sequence as A141158?

For a Pythagorean triple a,b,c, these primes (and 2) are the possible prime factors of 2a+b, |2a-b|, 2b+a, and 2b-a. - J. Lowell, Nov 05 2011

The prime factors of A028387 (n + (n+1)^2). - Richard R. Forberg, Dec 12 2014

a(n) =  A045468(n-1) for n > 1. - Robert Israel, Dec 22 2014

Except for p=5, these are primes p that divide Fibonacci(p-1). - Dmitry Kamenetsky, Jul 27 2015

REFERENCES

Borevich and Shafaewich, Number Theory.

D. B. Zagier, Zetafunktionen und quadratische Koerper.

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

C. Banderier, Calcul de (5/p)

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

FORMULA

a(n) ~ 2n log n. - Charles R Greathouse IV, Nov 29 2016

MAPLE

select(isprime, [5, seq(op([5*k-1, 5*k+1]), k=1..1000)]); # Robert Israel, Dec 22 2014

MATHEMATICA

Join[{5}, Select[Prime[Range[4, 100]], Mod[#, 5] == 1 || Mod[#, 5] == 4 &]] (* Alonso del Arte, Nov 27 2011 *)

PROG

(PARI) forprime(p=2, 1e3, if(kronecker(5, p)>=0, print1(p", "))) \\ Charles R Greathouse IV, Jun 16 2011

(MAGMA) [ p: p in PrimesUpTo(700) | p mod 5 in {0, 1, 4}]; // Vincenzo Librandi, Aug 21 2012

CROSSREFS

Cf. A045468, A141111, A141112 (d=65).

Cf. A003631 (complement with respect to A000040).

Sequence in context: A089270 A275068 * A141158 A239732 A130828 A244241

Adjacent sequences:  A038869 A038870 A038871 * A038873 A038874 A038875

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

Corrected and extended by Peter K. Pearson, May 29 2005

Edited by N. J. A. Sloane, Jul 28 2008 at the suggestion of R. J. Mathar

STATUS

approved

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Last modified June 22 12:17 EDT 2017. Contains 288613 sequences.