OFFSET
1,1
COMMENTS
It's easy to see that all terms = 1 modulo 12. Primes p are {1,5,7,11} mod 12. Then p+1 = {2,6,8,12} mod 12 and only 2 mod 12 may give semiprime. Cf. A186696 for values of (a(n)-1)/12 = 5,6,16,23,33,35, etc.
LINKS
Zak Seidov, Table of n, a(n) for n = 1..1000
EXAMPLE
61 is prime, 62=2*31 is semiprime, 63=3*3*7 is 3-almost prime.
MATHEMATICA
Do[p=Prime[n]; If[Total[FactorInteger[p+1]][[2]]==2&&Total[FactorInteger[p+2]][[2]]==3, Print[p]], {n, 1, 1000}];
PROG
(PARI) list(lim)=my(v=List(), L=(lim+2)\3, t); forprime(p=3, L\3, forprime(q=3, min(L\p, p), t=3*p*q-2; if(t%12==1 && isprime(t) && isprime((t+1)/2), listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Feb 01 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Zak Seidov, Jan 03 2006
EXTENSIONS
Extended and edited by Charles R Greathouse IV, Apr 20 2010
STATUS
approved