OFFSET
1,1
COMMENTS
Subsequence of A112998: a(1) = 193 = A112998(3), a(2) = 421= A112998(6), a(3) = 661 = A112998(8). - Zak Seidov, Oct 14 2012
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..2000
EXAMPLE
193 is prime, 194=2*97 is semiprime, 195=3*5*13 is 3-almost prime, 196=2*2*7*7 is 4-almost prime.
MATHEMATICA
Do[p=Prime[n]; If[Table[Total[FactorInteger[p+k]][[2]], {k, 3}]=={2, 3, 4}, Print[p]], {n, 1, 10000}]
PROG
(Magma) [n: n in PrimesUpTo(5*10^4) | forall{k: k in [1..3] | &+[f[j, 2]: j in [1..#f]] eq k+1 where f is Factorization(n+k)}]; // Vincenzo Librandi, Sep 24 2012
(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) && bigomega(t+3)==4, listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Feb 01 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Zak Seidov, Jan 03 2006
EXTENSIONS
Edited by Charles R Greathouse IV, Apr 20 2010
STATUS
approved