[go: up one dir, main page]

login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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