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

Author

Giovanni Teofilatto, Apr 21 2010

Keywords

• nonn
• changed

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

Programs

Mathematica

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

Extensions

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

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