OFFSET
1,1
COMMENTS
Also primes of the form (p*q - 1)/2, where p and q are distinct primes.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
FORMULA
2*a(n)+1 = A233561(n). - R. J. Mathar, Aug 30 2016
EXAMPLE
7 is in the sequence because it is prime and 7*2 + 1 = 15 = 3*5 is a semiprime.
MATHEMATICA
t = Select[Range[1, 7000, 2], Map[Last, FactorInteger[#]] == Table[1, {2}] &]; Take[(t - 1)/2, 120] (* A234093 *)
v = Flatten[Position[PrimeQ[(t - 1)/2], True]] ; w = Table[t[[v[[n]]]], {n, 1, Length[v]}] (* A233561 *)
(w - 1)/2 (* A234095 *) (* Peter J. C. Moses, Dec 23 2013 *)
Select[Prime[Range[200]], PrimeOmega[2#+1]==2&] (* Harvey P. Dale, Mar 19 2015 *)
PROG
(PARI) is(n)=isprime(n) && bigomega(2*n+1)==2 \\ Charles R Greathouse IV, Feb 19 2014
(Magma) IsSemiprime:=func< p | &+[ k[2]: k in Factorization(p)] eq 2 >; [p: p in PrimesUpTo(1000)| IsSemiprime(2*p+1)]; // Vincenzo Librandi, Feb 21 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Dec 27 2013
EXTENSIONS
New name from Zak Seidov, Feb 19 2014
STATUS
approved