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%I #17 Sep 08 2022 08:45:23
%S 193,421,661,1093,1657,2137,2341,2593,6217,7057,8101,9817,12421,12853,
%T 15121,16033,16417,17257,17881,19813,20641,21817,25033,25657,27337,
%U 28921,30661,31081,31321,31333,32377,35521,36457,38281,40693,45553
%N Numbers n such that n, n+1, n+2 and n+3 are 1,2,3,4-almost primes.
%C Subsequence of A112998: a(1) = 193 = A112998(3), a(2) = 421= A112998(6), a(3) = 661 = A112998(8). - _Zak Seidov_, Oct 14 2012
%H Vincenzo Librandi, <a href="/A113000/b113000.txt">Table of n, a(n) for n = 1..2000</a>
%e 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.
%t Do[p=Prime[n];If[Table[Total[FactorInteger[p+k]][[2]], {k, 3}]=={2, 3, 4}, Print[p]], {n, 1, 10000}]
%o (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
%o (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
%Y Cf. A112998.
%K nonn,easy
%O 1,1
%A _Zak Seidov_, Jan 03 2006
%E Edited by _Charles R Greathouse IV_, Apr 20 2010
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