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A117969
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Start of least run of maximal length of consecutive n-almost primes.
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0
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OFFSET
| 1,1
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COMMENTS
| For n>=2 there cannot be more than 2^n - 1 consecutive n-almost primes. Is it known whether there always exists such a run of length 2^n - 1? If not, I conjecture so. This is confirmed to be true for terms through a(4). Terms here equal the last terms of corresponding finite sequences: a(3) = A067813(6). a(4) was computed by Don Reble as A067814(14). a(5) >= A067820(12).
a(4) is smaller than the number 488995430567765317569 found by Forbes. [From T. D. Noe (noe(AT)sspectra.com), Oct 29 2008]
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REFERENCES
| Tony Forbes, Fifteen consecutive integers with exactly four prime factors, Math. Comp. 71 (2002), 449-452. [From T. D. Noe (noe(AT)sspectra.com), Oct 29 2008]
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EXAMPLE
| a(2) = 33 because 33, 34, 35 is the least run of three consecutive 2-almost primes (semiprimes).
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CROSSREFS
| Cf. A067813, A067814, A067820, A067821, A067822.
Sequence in context: A083459 A034173 A132519 * A003820 A112980 A109336
Adjacent sequences: A117966 A117967 A117968 * A117970 A117971 A117972
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KEYWORD
| hard,nonn
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AUTHOR
| Rick L. Shepherd (rshepherd2(AT)hotmail.com), Apr 05 2006
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