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 A113000 Numbers n such that n, n+1, n+2 and n+3 are 1,2,3,4-almost primes. 6
 193, 421, 661, 1093, 1657, 2137, 2341, 2593, 6217, 7057, 8101, 9817, 12421, 12853, 15121, 16033, 16417, 17257, 17881, 19813, 20641, 21817, 25033, 25657, 27337, 28921, 30661, 31081, 31321, 31333, 32377, 35521, 36457, 38281, 40693, 45553 (list; graph; refs; listen; history; text; internal format)
 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 CROSSREFS Cf. A112998. Sequence in context: A065213 A100363 A142500 * A105129 A140631 A142117 Adjacent sequences:  A112997 A112998 A112999 * A113001 A113002 A113003 KEYWORD nonn,easy AUTHOR Zak Seidov, Jan 03 2006 EXTENSIONS Edited by Charles R Greathouse IV, Apr 20 2010 STATUS approved

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