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A056809
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Numbers n such that n, n+1 and n+2 are products of two primes.
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23
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33, 85, 93, 121, 141, 201, 213, 217, 301, 393, 445, 633, 697, 841, 921, 1041, 1137, 1261, 1345, 1401, 1641, 1761, 1837, 1893, 1941, 1981, 2101, 2181, 2217, 2305, 2361, 2433, 2461, 2517, 2641, 2721, 2733, 3097, 3385, 3601, 3693, 3865, 3901, 3957, 4285
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Each term is the beginning of a run of three 2-almost primes (semiprimes). No runs exist of length greater than three. For the same reason, each term must be odd: If n were even, then so would be n+2. In fact, one of n or n+2 would be divisible by 4, so must indeed be 4 to have only two prime factors. However, neither 2,3,4 nor 4,5,6 is such a run. - Rick L. Shepherd (rshepherd2(AT)hotmail.com), May 27 2002
n+1, which is twice a prime, is in A086005. The primes are in A086006. - T. D. Noe (noe(AT)sspectra.com), May 31 2006
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LINKS
| D. W. Wilson, Table of n, a(n) for n = 1..10000
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EXAMPLE
| 121 is in the sequence because 121 = 11^2, 122 = 2*61 and 123 = 3*41, each of which is the product of two primes.
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MATHEMATICA
| f[n_] := Plus @@ Transpose[ FactorInteger[n]] [[2]]; Select[Range[10^4], f[ # ] == f[ # + 1] == f[ # + 2] == 2 & ]
f[n_]:=Last/@FactorInteger[n]=={1, 1}||Last/@FactorInteger[n]=={2}; Timing[lst={}; Do[If[f[n]&&f[n+1]&&f[n+2], AppendTo[lst, n]], {n, 2, 8!}]; lst] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 25 2010]
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PROG
| (PARI) forstep(n=1, 5000, 2, if(bigomega(n)==2 && bigomega(n+1)==2 && bigomega(n+2)==2, print1(n, ", ")))
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CROSSREFS
| Cf. A070552, A045939, A039833.
Sequence in context: A044171 A044552 A045939 * A073251 A005238 A052214
Adjacent sequences: A056806 A056807 A056808 * A056810 A056811 A056812
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KEYWORD
| nonn
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AUTHOR
| Sharon Sela (sharonsela(AT)hotmail.com), May 04 2002
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EXTENSIONS
| Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), May 04 2002
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