OFFSET
1,1
COMMENTS
Discriminant=-55.
Primes p such that x^4 - 2x^3 + x - 1 has no integer roots modulo p^2. According to the Bunyakovsky conjecture, there are infinitely many such primes. - Griffin N. Macris, Jul 21 2016
LINKS
Vincenzo Librandi and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi]
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)
Wikipedia, Bunyakovsky conjecture
EXAMPLE
89 is in the sequence since it is prime and with x=5 and y=-1, 4x^2 + 3xy + 4y^2 = 4*5^2 + 3*5*(-1) + 4*(-1)^2 = 100 - 15 + 4 = 89. - Michael B. Porter, Jul 22 2016
MAPLE
N:= 10000: # to get all terms <= N
S:= {}:
for y from 0 to floor(sqrt(16*N/55)) do
s:= floor(sqrt(16*N-55*y^2));
S:= S union select(isprime, {seq(4*x^2 + 3*x*y + 4*y^2,
x = ceil((-s-3*y)/8) .. floor((s-3*y)/8))})
od:
sort(convert(S, list)); # Robert Israel, Jul 21 2016
MATHEMATICA
Union[QuadPrimes2[4, 3, 4, 10000], QuadPrimes2[4, -3, 4, 10000]] (* see A106856 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
T. D. Noe, May 09 2005
STATUS
approved