OFFSET
1,1
COMMENTS
The first 14 terms correspond to n from 0 to 13, which makes 8*n^2+8*n+31 a prime-generating polynomial (see the link).
This is a prime-generating polynomial of the form c*n^2+c*n+p, where c=2^k (k=0,1,2...) and p is prime with c and p containing at most two digits. Prime-generating polynomials of this kind arise for k=0,1,2,3 - see A005846 and A007635 (k=0), A007639 (k=1), and A048988 (k=2).
All terms are of the form 4m+3. Terms 1 and 4 are Mersenne primes (A000668).
LINKS
Eric Weisstein's World of Mathematics, Prime-Generating Polynomial
EXAMPLE
79 is a term as it is a prime corresponding to n=2: 8*4+8*2+31=79.
MATHEMATICA
Select[Range[0, 100]//8#^2+8#+31&, PrimeQ]
PROG
(PARI) for(n=0, 100, isprime(p=8*n^2+8*n+31)&& print1(p ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Waldemar Puszkarz, Oct 06 2017
STATUS
approved