[seqfan] Re: Sets of composite numbers

[Frank Adams-Watters]

Sorry, A075067 is looking for exact, and it appears to be correct.

There are actually three sequences for cases like this:

1) Find the lengths of runs, determine the first one with length 
exactly n, and take its first element.

2) Find the lengths of runs, determine the first one with length at 
least n, and take its first element.

3) Find the first value such that it and the next n-1 values have the 
property, but the next number does not.

I have seen all three of these in the OEIS, for various properties, but 
never all three for the same property.

A075067 is case (1), and as noted appears to be correct.

A189118 appears to be an attempt at (3), but has been restricted to be 
increasing. This is probably an accident, the Mathematica code is 
starting each search where the last one left off, overlooking the 
possibility than a(n+1) < a(n) for this case.

There does not appear to be any attempted implementation of (2) in the 
database for this property.

Probably the definition of A189118 should be changed, and a corrected 
version added to the database. Perhaps case (2) should also be added.

-----
Note, by the way, that the problem without specifying that the 
composites be odd is essentially the same. The even numbers other than 
2 are all composite, so each run of m odd composites is, when the 
adjacent even numbers are included, a run of 2m+1 composites.

Franklin T. Adams-Watters

-----Original Message-----
From: Frank Adams-Watters <franktaw at netscape.net>


First, note that these are different: A075067 claims to be looking for
at least n consecutive, while A189118 is looking for exactly n.

That said, I think both are wrong.

In A075067, a(4) through a(6) should all be 115. There are probably
further errors.

In A189118, a(4) is given as 119. But then a(5) should be 117 and a(6)
should be 115.

Franklin T. Adams-Watters

-----Original Message-----
From: L. Edson Jeffery <lejeffery2 at gmail.com>
To: seqfan <seqfan at list.seqfan.eu>
Sent: Mon, Jul 28, 2014 10:26 pm
Subject: [seqfan] Re: Sets of composite numbers


For consecutive odd composites, see https://oeis.org/A075067 and
https://oeis.org/A189118, but which of the two is correct?

Ed Jeffery

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