A117969 - OEIS

%I #8 Oct 19 2017 10:43:05

%S 2,33,211673,97524222465

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

%C 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).

%C a(4) is smaller than the number 488995430567765317569 found by Forbes. [From _T. D. Noe_, Oct 29 2008]

%H Tony Forbes, <a href="https://doi.org/10.1090/S0025-5718-01-01321-7">Fifteen consecutive integers with exactly four prime factors</a>, Math. Comp. 71 (2002), 449-452. [From _T. D. Noe_, Oct 29 2008]

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

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

%K hard,nonn

%O 1,1

%A _Rick L. Shepherd_, Apr 05 2006