A176617 -id:A176617 - cp's OEIS frontend

A176622 Primes of the form x^2 + 17*y^2, where x and y=x+1 are consecutive natural numbers.

17, 157, 281, 4021, 8669, 10321, 14057, 16141, 37997, 58369, 71317, 78277, 80669, 93169, 109357, 112181, 117937, 136069, 176221, 179801, 187069, 198241, 213641, 225569, 237821, 285517, 299281, 318137, 393977, 410117, 443369, 507697, 513761

Offset: 1

Giovanni Teofilatto, Apr 22 2010

nonn

a(n) is congruent 1 mod 4.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A176608, A176616, A176617.

[a: n in [1..250]|IsPrime(a) where a is 18*n^2+34*n+17] // Vincenzo Librandi, Dec 04 2010

Select[Table[18x^2+34x+17,{x,0,200}],PrimeQ] (* Harvey P. Dale, May 06 2017 *)

Constraint y=x+1 added to definition by R. J. Mathar, May 04 2010

Extended by Vincenzo Librandi, Apr 25 2010

A176695 Primes of the form x^2 + 29*(x+1)^2.

Original entry on oeis.org

29, 1069, 4297, 7649, 18701, 21817, 34613, 45553, 52837, 60661, 63389, 71933, 77929, 81017, 90641, 107881, 111509, 122753, 155377, 168601, 187073, 201557, 264893, 369409, 376097, 438989, 476029, 498973, 579353, 674701, 711173, 767681

Offset: 1

Giovanni Teofilatto, Apr 24 2010

nonn

a(n) == 1 (mod 4).

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A176608, A176616, A176617.

[ a: n in [0..250] | IsPrime(a) where a is 30*n^2+58*n+29 ] // Vincenzo Librandi, Apr 25 2010

Select[Table[x^2 + 29(x + 1)^2, {x, 0, 200}], PrimeQ] (* Harvey P. Dale, Dec 12 2010 *)

Corrected and extended by Vincenzo Librandi, Apr 25 2010

cp's OEIS Frontend

A176622 Primes of the form x^2 + 17*y^2, where x and y=x+1 are consecutive natural numbers.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

Extensions