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A113000
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Numbers n such that n, n+1, n+2 and n+3 are 1,2,3,4-almost primes.
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6
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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
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OFFSET
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1,1
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COMMENTS
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Subsequence of A112998: a(1) = 193 = A112998(3), a(2) = 421= A112998(6), a(3) = 661 = A112998(8). - Zak Seidov, Oct 14 2012
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..2000
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EXAMPLE
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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.
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MATHEMATICA
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Do[p=Prime[n]; If[Table[Total[FactorInteger[p+k]][[2]], {k, 3}]=={2, 3, 4}, Print[p]], {n, 1, 10000}]
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PROG
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(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
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CROSSREFS
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Cf. A112998.
Sequence in context: A065213 A100363 A142500 * A105129 A140631 A142117
Adjacent sequences: A112997 A112998 A112999 * A113001 A113002 A113003
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KEYWORD
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nonn,easy
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AUTHOR
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Zak Seidov, Jan 03 2006
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EXTENSIONS
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Edited by Charles R Greathouse IV, Apr 20 2010
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STATUS
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approved
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