OFFSET
1,2
COMMENTS
Numbers k such that 2*k+1 and 4*k^2 - 2*k + 1 are both prime.
Same as k/2 such that k^3 + 1 is a semiprime, because then k must be even.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Semiprime.
Wikipedia, Semiprime.
EXAMPLE
(2*1)^3 + 1 = 9 = 3*3 is a semiprime, so a(1) = 1.
MATHEMATICA
Select[Range[800], PrimeQ[(2 #)^2 - 2 # + 1] && PrimeQ[2 # + 1] &]
Select[Range[800], PrimeOmega[(2#)^3+1]==2&] (* Harvey P. Dale, Nov 28 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Jonathan Sondow, Feb 02 2014
STATUS
approved