A107003 Primes of the form 24n + 5.

5, 29, 53, 101, 149, 173, 197, 269, 293, 317, 389, 461, 509, 557, 653, 677, 701, 773, 797, 821, 941, 1013, 1061, 1109, 1181, 1229, 1277, 1301, 1373, 1493, 1613, 1637, 1709, 1733, 1877, 1901, 1949, 1973, 1997, 2069, 2141, 2213, 2237, 2309, 2333, 2357, 2381, 2477

Offset

1,1

Comments

Primes of the form 5x^2+2xy+5y^2, with x and y any integer. Discriminant=-96. Also primes of the forms 5x^2+4xy+20y^2 and 5x^2+2xy+29y^2. See A140633. - T. D. Noe, May 19 2008

Also primes of the form -4*x^2+4*x*y+5*y^2, of discriminant -96 (as well as of the form 8*x^2+16*x*y+5*y^2). - Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (oscfalgan(AT)yahoo.es), Jun 28 2008

References

Z. I. Borevich and I. R. Shafarevich. Number Theory. Academic Press. 1966.

Links

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

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

Formula

a(n) ~ 8n log n. - Charles R Greathouse IV, Dec 07 2014

Example

29 is a member because we can write 29=-4*4^2+4*4*3+5*3^2 (or 29=8*1^2+16*1*1+5*1^2).

Mathematica

Union[QuadPrimes2[5, 2, 5, 10000], QuadPrimes2[5, -2, 5, 10000]] (* see A106856 *)

Prog

(PARI) select(n->n%24==5, primes(1000)) \\ Charles R Greathouse IV, Dec 07 2014

Crossrefs

Cf. A141373, A141375, A141376 (d = -96).

Sequence in context: A201712 A271923 A224499 * A141374 A147153 A300777

Adjacent sequences: A107000 A107001 A107002 * A107004 A107005 A107006

Keyword

nonn,easy

Author

T. D. Noe, May 09 2005

Extensions

Name and comment switched by Charles R Greathouse IV, Dec 07 2014

Edited by N. J. A. Sloane, Jul 14 2019

Status

approved