OFFSET
1,1
COMMENTS
Discriminant = 44. Class = 2. Binary quadratic forms a*x^2 + b*x*y + c*y^2 have discriminant d = b^2 - 4ac.
Also, primes of the form u^2 - 11v^2. The transformation {u, v} = {x+3y, y} yields the form in the title. - Tito Piezas III, Dec 28 2008
Also primes p == 1 (mod 4) and == 1, 3, 4, 5 or 9 (mod 11). - Juan Arias-de-Reyna, Mar 20 2011.
REFERENCES
Z. I. Borevich and I. R. Shafarevich, Number Theory.
LINKS
Juan Arias-de-Reyna, Table of n, a(n) for n = 1..10000
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS: Index to related sequences, programs, references. OEIS wiki, June 2014.
D. B. Zagier, Zetafunktionen und quadratische Körper, Springer, 1981.
EXAMPLE
a(3)=53 because we can write 53=5^2+6*5*1-2*1^2 (or 53=5*1^2+8*1*4+4^2)
MATHEMATICA
Select[Prime[Range[250]], MatchQ[Mod[#, 44], Alternatives[1, 5, 9, 25, 37]] &] (* Jean-François Alcover, Oct 28 2016 *)
PROG
(PARI) isA141182(p) = p%4==1 & issquare(Mod(p, 11)) \\ M. F. Hasler, Mar 20 2011
CROSSREFS
KEYWORD
nonn
AUTHOR
Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (lourdescm84(AT)hotmail.com), Jun 12 2008
STATUS
approved