Observation on A053669

[zak seidov]

Yes, 
and because a(n_odd)=2
keep only even n's.
Zak

--- Richard Mathar <mathar at strw.leidenuniv.nl> wrote:

> 
> dww> From seqfan-owner at ext.jussieu.fr  Sat Nov  4
> 21:12:32 2006
> dww> Return-Path: <seqfan-owner at ext.jussieu.fr>
> dww> From: "David Wilson" <davidwwilson at comcast.net>
> dww> To: "Sequence Fans" <seqfan at ext.jussieu.fr>
> dww> Subject: Observation on A053669
> dww> ...
> dww> It seems to me that
> dww> 
> dww> %N A053669 Smallest prime co-prime to n.
> dww> 
> dww> could just as easily be described
> dww> 
> dww> %N A053669 Smallest number > 1 coprime to n.
> dww> 
> dww> and the fact that a(n) is prime falls out. 
> This definition would also =
> dww> simplify the program.
> dww>...
> 
> Yes. If the smallest prime co-prime to n would not
> be a prime,
> it would be built by at least two prime factors, the
> smaller of which
> would be the correct entry (proof by reductio ad
> absurdum).
> 
> It would still be useful to keep in a comment that
> the numbers are all prime
> (this might speed up some searches for the
> numbers...)
> 
> I'd propose to list in a comment the first
> occurrences of the first primes:
> first 5 at a(6)
> first 7 is a(30)
> first 11 is a(210)
> first 13 is a(2310)
> first 17 is a(30030)
> first 19 is a(510510)
> where the indices are 6=2*3, 30=2*3*5, 210=2*3*5*7,
> 2*3*5*7*11 etc,
> (the primorials, I guess, as in A002110)
> 
> -- RJM
> 



 
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