[seqfan] The new sequence A294673 and a connection to the mysterious A163778

Neil Sloane njasloane at gmail.com
Fri Nov 10 10:41:25 CET 2017


The other day I cleaned up the definition of a new sequence that had been
submitted, A294673, which now seems very interesting.

There is now a conjecture from Andrew Howroyd that the max values in
A294673 occur at positions given in A163778. I don't disagree, but the
definition of A163778 is hard to follow and seems to depend on the value of
Pi !!  I wish someone would improve the definition of that sequence, and
maybe give a picture of the mysterious spiral that it uses. That sequence
also needs more terms (and some programs).

There is also a conjecture from Andrey Zabolotskiy that A294673 is a
bisection of A003558, which would explain the values.  It would nice to
have proofs of these conjectures.

The subject of A294673 is the order of a certain shuffle permutation of a
deck of 2n+1 cards, the "inside-out" permutation, somewhat related to the
Mongean shuffle, so presumably the answers to these questions are known to
group theorists.



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