OFFSET
1,1
COMMENTS
It is easy to prove that all the terms except the first two must satisfy a(n) mod 10 = 9.
EXAMPLE
a(3) = 29 = p and 2*p + 1 = 59 and (59^2 + 1)/2 = 29^2 + 30^2 = 1741 are prime.
MATHEMATICA
Flatten[Append[{2, 5}, Select[Sort[Range[29, 30000000, 30], Range[49, 30000000, 30]], PrimeQ[ # ]&&PrimeQ[2 # + 1] && PrimeQ[1 + 2 # + 2 #^2] &]]] (Zak Seidov)
f1[n_]:=(n+1)^2-n^2; f2[n_]:=(n+1)^2+n^2; Select[Prime[Range[8! ]], PrimeQ[f1[ # ]]&&PrimeQ[f2[ # ]]&] (* Vladimir Joseph Stephan Orlovsky, Feb 25 2010 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Robin Garcia, Sep 29 2004
EXTENSIONS
More terms from Zak Seidov, Feb 16 2005
STATUS
approved