OFFSET
3,1
COMMENTS
For primes p other than 3, p == 1 or 2 (mod 3) and p^2 == 1 (mod 3). Thus 2*p^2 + 1 is a multiple of 3.
LINKS
G. C. Greubel, Table of n, a(n) for n = 3..1000
FORMULA
Product_{n >= 3} (3*a(n) + 1) / (3*a(n) - 1) = (26/25) * (50/49) * (122/121) * ... = 54/(5*Pi^2) = 1.0942687833372479315938982026650585002 (constant).
a(3) = 17; a(n + 1) = a(n) + 16 * A075888(n-2) for n > 3.
MATHEMATICA
(2Prime[Range[3, 50]]^2 + 1)/3 (* Alonso del Arte, May 12 2017 *)
PROG
(PARI) {
forprime(n=5, 300,
print1((2*n^2+1)/3", ")
)
}
(Magma) [(2*NthPrime(n)^2+1)/3: n in [3..50]]; // Vincenzo Librandi, May 15 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Dimitris Valianatos, May 12 2017
STATUS
approved