[seqfan] Re: Canonical bijection from positive integers to positive rationals.

[Antti Karttunen]

On 3/3/20, Frank Adams-watters via SeqFan <seqfan at list.seqfan.eu> wrote:
> I still haven't gotten any answers to my fundamental question: how do I
> enter a function defined on the positive rationals into the database? Should
> I just pick one of these bijections to use?
>

I would use A002487(n)/A002487(1+n) and maybe also Sagher-map
A071974(n)/A071975(n) that was suggested by Peter, especially if the
synergetic effect (with your chosen function) is something elegant
(just my intuition, as both num & den of the latter are
multiplicative).

I guess the range of your functions is in Q? So one could store both
the fraction's num and den (as is usual for fractions), but for any
such fraction sequence, we could (also) "compress" that information to
just the index n in the sequence of fractions like
A002487(n)/A002487(1+n) or A071974(n)/A071975(n) (sometimes this could
even reduce to something very simple?)


Best,

Antti


> Franklin T. Adams-Watters
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