[seqfan] Re: zig-zag pseudoprimes
shevelev at bgu.ac.il
Wed Sep 1 16:19:27 CEST 2010
Nevertheless, I did not understand if you really obtained that, e.g., A000111(561)==1(mod 561)?
----- Original Message -----
From: Richard Mathar <mathar at strw.leidenuniv.nl>
Date: Wednesday, September 1, 2010 14:29
Subject: [seqfan] Re: zig-zag pseudoprimes
To: seqfan at seqfan.eu
> Followup on http://list.seqfan.eu/pipermail/seqfan/2010-
> September/005897.html :
> > Recently I proved (not basing on Fermat little theorem)
> that if n==1(mod 4) is prime, then
> > A000111(n)==1(mod n); if n==3(mod 4) is prime, then
> A000111(n)==-1(mod n).
> > I call possible composite numbers m with such property "zig-
> zag pseudoprimes".
> Numbers n such that A000111(n) == 1 mod (n) are
> Intersecting with A016813 (4n+1), then removing the set of
> A002144 (primes 4n+1),
> the composites 561, 781, 1105... remain (which one can look up
> in the OEIS,
> perhaps A122782, A020142, A020174 etc).
> For the case of composites n == 3 ( mod 4) with A000111(n) == -1
> (mod n)
> we have at least the case n = 91 (no other <= 850)
> This is all subject to checking by an independent committee. I
> can submit them,
> but I shall not. (I do not submit sequences invented by other people.)
> Richard Mathar
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