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

2, 33, 211673, 97524222465

Offset

1,1

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]

Links

Table of n, a(n) for n=1..4.

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

Example

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

Crossrefs

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

Sequence in context: A368899 A034173 A132519 * A003820 A112980 A109336

Adjacent sequences: A117966 A117967 A117968 * A117970 A117971 A117972

Keyword

hard,nonn

Author

Rick L. Shepherd, Apr 05 2006

Status

approved