Duplicate sequences with error

[franktaw at netscape.net]

It appears that A093551 ("a(n) is the smallest number m such that m+k 
is the product of k+1 primes for k=0,1,2,...,n. ") is an erroneous 
version of A072875 ("Smallest start for a run of n consecutive numbers 
of which the i-th has exactly i prime factors.").  A093551(7) is 
greater then A072875(8) [the offsets for the sequences differ].  I have 
verified that A072875(8) = 19896463921 does satisfy the condition, 
which shows that A093551 is incorrect.

A093551 includes a Mathematica program.  It looks like this program is 
assuming that the kth term in the sequence of consecutive values is 
divisible by k; this is not necessarily the case (although it is true 
for k <= 4 - looking at A072875, it appears to be true for k = 5 as 
well, but I don't see why that should be necessary; it would seem that 
values could be congruent to 13 or 17 mod 20 as well).

(The corresponding sequence looking at the number of distinct prime 
divisors is A086560, which is quite different; this is not the problem. 
  Incidently, I think the conjecture in A086560 - that the sequence is 
finite - is almost certainly false.)

Franklin T. Adams-Watters

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