OFFSET
1,1
COMMENTS
Primes of form p*q + 2, where p and q are primes.
11 is the only prime of this form where p=q. For prime p>3, 3 divides p^2+2. - T. D. Noe, Mar 01 2006
The asymptotic growth of this sequence is relevant for A204142. We have a(10^k) = (11, 79, 1571, 27961, 407741, 5647823, ...). - M. F. Hasler, Feb 13 2012
LINKS
M. F. Hasler, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = A241809(n) + 2. - Hugo Pfoertner, Oct 30 2023
MATHEMATICA
Take[Select[ # + 2 & /@ Union[Flatten[Outer[Times, Prime[Range[100]], Prime[Range[100]]]]], PrimeQ], 60]
Select[Prime[Range[200]], PrimeOmega[#-2]==2&] (* Paolo Xausa, Oct 30 2023 *)
PROG
(PARI) n=0; for (m=2, 10^9, p=prime(m); if (bigomega(p - 2) == 2, write("b063638.txt", n++, " ", p); if (n==1000, break))) \\ Harry J. Smith, Aug 26 2009
(PARI) forprime(p=3, 9999, bigomega(p-2)==2 & print1(p", "))
(PARI) p=2; for(n=1, 1e4, until(bigomega(-2+p=nextprime(p+1))==2, ); write("b063638.txt", n" "p)) \\ M. F. Hasler, Feb 13 2012
(PARI) list(lim)=my(v=List(), t); forprime(p=3, (lim-2)\3, forprime(q=3, min((lim-2)\p, p), t=p*q+2; if(isprime(t), listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Aug 05 2016
(Haskell)
a063638 n = a063638_list !! (n-1)
a063638_list = map (+ 2) $ filter ((== 1) . a064911) a040976_list
-- Reinhard Zumkeller, Feb 22 2012
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jul 21 2001
STATUS
approved