A176608 Primes of the form x^2 + 5*y^2, where x and y=x+1 are consecutive natural numbers.

5, 89, 281, 1321, 2129, 2861, 3701, 4649, 6469, 6869, 9049, 9521, 10501, 13729, 17389, 18041, 19381, 21481, 23689, 26801, 28429, 33601, 42169, 71069, 75041, 81901, 86161, 90529, 92009, 101141, 104281, 113989, 129361, 131129, 153281, 157141, 163021, 169009, 171029, 200569, 209441, 213949, 259169, 274349, 282101, 314189, 339389, 371509, 374501, 383549, 417649

Offset

1,1

Comments

Terms are congruent to 1 mod 4.

Also primes of the form 6*x^2+10*x+5.

If one were to take the sum of all numbers in the open interval between n^2 and (n+1)^2 and called this sum A and did the same for (n+1)^2 and (n+2)^2 and called this sum B, then B-A is a prime, resulting from the same 6*n^2 + 10*n + 5. - J. M. Bergot, Jun 11 2011

Links

Table of n, a(n) for n=1..51.

Mathematica

Select[Table[x^2+5(x+1)^2, {x, 0, 500}], PrimeQ] (* Harvey P. Dale, Dec 16 2010 *)

Crossrefs

Sequence in context: A139937 A059696 A072216 * A277233 A167735 A221517

Adjacent sequences: A176605 A176606 A176607 * A176609 A176610 A176611

Keyword

nonn

Author

Giovanni Teofilatto, Apr 21 2010

Extensions

Provided less ambiguous definition - R. J. Mathar, May 04 2010

More terms from Vincenzo Librandi and R. J. Mathar, Apr 21 2010

Status

approved