A117969 Start of least run of maximal length of consecutive n-almost primes.

2, 33, 211673, 97524222465

Offset: 1

Author

Rick L. Shepherd, Apr 05 2006

Keywords

• hard
• nonn

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, Oct 29 2008]

Examples

			a(2) = 33 because 33, 34, 35 is the least run of three consecutive 2-almost primes (semiprimes).
		

Links

• Tony Forbes, Fifteen consecutive integers with exactly four prime factors, Math. Comp. 71 (2002), 449-452. [From _T. D. Noe_, Oct 29 2008]

Crossrefs

Cf. A067813, A067814, A067820, A067821, A067822.