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A038872
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Primes congruent to {0, 1, 4} mod 5.
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64
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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; internal format)
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OFFSET
| 1,1
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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). Discriminant = 5. Class = 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 that this coincides with the present sequence, Jul 22 2008
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
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REFERENCES
| Borevich and Shafaewich, Number Theory.
D. B. Zagier, Zetafunktionen und quadratische Koerper.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
C. Banderier, Calcul de (5/p)
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MATHEMATICA
| Join[{5}, Select[Prime[Range[4, 100]], Mod[#, 5] == 1 || Mod[#, 5] == 4 &]] (* Alonso del Arte, Nov 27 2011 *)
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PROG
| (PARI) print1(5); forprime(p=9, 1e3, if((k->k==1|k==4)(p%5), print1(", "p))) \\ Charles R Greathouse IV, Jun 16 2011
(PARI) forprime(p=2, 1e3, if(kronecker(5, p)>=0, print1(p", "))) \\ Charles R Greathouse IV, Jun 16 2011
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CROSSREFS
| Cf. A141111, A141112 (d=65).
Sequence in context: A132087 A089270 * A141158 A130828 A108151 A088059
Adjacent sequences: A038869 A038870 A038871 * A038873 A038874 A038875
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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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.
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