Observation on A053669

[Richard Mathar]

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