[seqfan] Re: zig-zag pseudoprimes

[Vladimir Shevelev]

Very thanks, Doug!

Your conjecture about Carmichael numbers seems very interesting.
On the other hand, it is interesting to consider also sequences:
1) Non-Carmichael zig-zag pseudoprimes: according your calculations, 91 781 1661 2737
2) 4n+3 zig-zag pseudoprimes: 91, 8911
It is known that thre are "many" Carmichael pseudoprimes and, if your conjecture is true, we have also "many" 4n+1 zig-zag pseudoprimes. Therefore,  the most interesting sequence of zig-zag pseudoprimes remains sequence 2).  Can you continue it?

Best regards,
Vladimir 

----- Original Message -----
From: Douglas McNeil <mcneil at hku.hk>
Date: Wednesday, September 1, 2010 17:29
Subject: [seqfan] Re: zig-zag pseudoprimes
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>

> > This is all subject to checking by an independent committee.
> 
> I find the sequence begins
> 
> [91, 561, 781, 1105, 1661, 1729, 2465, 2737, 2821, 6601, 8911, 
> 10585, 15841]
> 
> which starts exactly the way predicted.  It also seems every
> Carmichael number <= 512461 is a zig-zag pseudoprime, and the
> non-Carmichael numbers seen so far show up in other pseudoprime
> sequences.
> 
> 
> Doug
> 
> -- 
> Department of Earth Sciences
> University of Hong Kong
> 
> 
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 Shevelev Vladimir‎