[seqfan] Re: A159559

[Benoît Jubin]

I agree that setting a(1)=2 is natural (taking a(1)=1 gives the
positive integers, of course).
What do you think of this definition:
a(1)=2 and for n>1, if n is prime (resp. composite) then a(n) is the
smallest prime (resp. composite) greater than a(n-1).

Benoit

On Tue, Jul 28, 2009 at 6:10 PM, Leroy Quet<q1qq2qqq3qqqq at yahoo.com> wrote:
>
> CCed to seqfan:
>
> Neil: Should something be done about A159559?
>
> The definition should probably be made more clear, especially since I think this is an important sequence.
> Maybe the definition should simply be something along the lines of:
> "If n = a prime, then a(n) = the smallest prime > a(n-1).
> If n = a composite, then a(n) = the smallest composite > a(n-1)."
>
> That definition takes up more characters, I think, than the original, but it surely is less ambiguous.
>
> Also, I would start the sequence with a 2 and give an offset of 1, with the case of a(1) be considered exceptional and not following the rule in the formula. But maybe the way the sequence is given (offset of 2) would be considered by you to be more natural, or not.
> If you think the sequence should start with a(1)=2, then add "a(1)=2" to the definition, of course. Otherwise, add a(2)=3".
>
> In any case, I wish someone would extend this sequence, possibly adding a b-file.
>
> Thanks,
> Leroy Quet
>
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