[seqfan] Re: A sequence from Johannes Kepler's "Harmonices Mundi"

Kevin Ryde user42_kevin at yahoo.com.au
Sun Feb 19 08:36:09 CET 2017

antti.karttunen at gmail.com (Antti Karttunen) writes:
> Mapping the unique fractions between such systems induces several
> permutations of natural numbers, e.g.: ... A258746 and A258996

They're flip every second bit (third highest downwards or second lowest
upwards) are they?  The note in A258996 about values abs(n-a(n)) being
2*A147992 should be the latter as +/-1 at alternate bit positions.
Similar in the downwards A258746 would then be union A147992 and
2*A147992 I expect.

> but probably not all combinations are yet in OEIS, or then appear under
> another guise.

All permutations exist back and forward between the 3 "high-to-low"
product trees starting 1/1 (5 seqs since A258746 is self-inverse).
Likewise all 5 back and forward between the 3 low-to-high trees.

A grep suggests the only cross-combination currently is bit reversal
A059893.  Others should be that plus one of the other perms.

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