OFFSET
1,1
COMMENTS
Conjecture: A084863(a(n))=1?
Is it true that a(n) = A019338(n+1)?
Comment: The truth of the conjecture A084863(a(n))=1 follows from the genus theory of quadratic forms (see Cox, page 61). By comparing enough terms, we see that the conjecture a(n) = A019338(n+1) is false. - T. D. Noe, May 02 2008
Appears to be the primes p such that (p mod 6)*(Fibonacci(p) mod 6)=25. - Gary Detlefs, May 26 2014
REFERENCES
David A. Cox, Primes of the Form x^2 + n y^2, Wiley, 1989.
LINKS
Vincenzo Librandi and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi]
Rick L. Shepherd, Binary quadratic forms and genus theory, Master of Arts Thesis, University of North Carolina at Greensboro, 2013.
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)
FORMULA
The primes are congruent to {2, 3, 5, 11} (mod 24). - T. D. Noe, May 02 2008 [The converse is also true via genus theory. - Jianing Song, Jul 11 2026]
EXAMPLE
A000040(17) = 59 = 32 + 27 = 2*4^2 + 3*3^2, therefore 59 is a term.
MATHEMATICA
QuadPrimes2[2, 0, 3, 10000] (* see A106856 *)
PROG
(PARI) list(lim)=my(v=List(), w, t); for(x=0, sqrtint(lim\2), w=2*x^2; for(y=0, sqrtint((lim-w)\3), if(isprime(t=w+3*y^2), listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Feb 09 2017
(PARI) isA084865(p) = isprime(p) && (p==2 || p==3 || p%24==5 || p%24==11) \\ Jianing Song, Jul 11 2026
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, Jun 10 2003
STATUS
approved
