# [seqfan] Re: Reciprocal Recaman

David Wilson davidwwilson at comcast.net
Mon Nov 18 04:46:06 CET 2013

```I hadn't seen A231692 since Don added the proof.  Very clever proof Don, one
for The Book.

Side note: I have always felt that proofs, examples, tables, &c, of more
than three or four lines should be submitted in an auxiliary file and linked
from the sequence rather than included textually in the sequence.

I am also curious if elements of A002805 and perhaps A231693 match
corresponding elements of A003418 infinitely often.

> -----Original Message-----
> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of M. F.
> Hasler
> Sent: Saturday, November 16, 2013 6:11 PM
> To: Sequence Fanatics Discussion list
> Subject: [seqfan] Re: Reciprocal Recaman
>
> On Sat, Nov 16, 2013 at 6:35 PM, David Wilson <davidwwilson at comcast.net>
> wrote:
> > But actually I was conjecturing that the partial sums of each sequence
> > of the form
> >
> >         1/1 +- 1/2 +- 1/3 +- 1/4 +- 1/5 +- ...
> >
> > are all distinct, not that the partial sums of distinct sequences are
> > distinct.
> >
> > So there. :-P
>
> That's of course what I understood, cf private mail ; but it is easy to
see that
> this is equivalent or at least a direct consequence of Don Reble's proof
given
> earlier on this list and in http://oeis.org/A231692, since if there were
two
> equal partial sums
> S(a) = S(a+n), then
> 0 = S(a+n)-S(a) = sum(k=a+1...a+n, epsilon(k) / k ) would be a counter-
> example.
>
> Maximilian
>
> >
> >> -----Original Message-----
> >> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of
> >> David Wilson
> >> Sent: Saturday, November 16, 2013 3:45 PM
> >> To: 'Sequence Fanatics Discussion list'
> >> Subject: [seqfan] Re: Reciprocal Recaman
> >>
> >> Well, it didn't take 400 years to disprove that one.
> >>
> >> > -----Original Message-----
> >> > From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of M.
> F.
> >> > Hasler
> >> > Sent: Saturday, November 16, 2013 2:08 PM
> >> > To: Sequence Fanatics Discussion list
> >> > Subject: [seqfan] Re: Reciprocal Recaman
> >> >
> >> > On Sat, Nov 16, 2013 at 12:26 PM, David Wilson
> >> > <davidwwilson at comcast.net> wrote:
> >> > > The partial sums of
> >> > >         1/1 +- 1/2 +- 1/3 +- 1/4 +- 1/5 +- ...
> >> > > are distinct for any choice of signs.
> >> >
> >> > Since this is formulated in a slightly ambiguous way, you may
> >> > easily
> >> defend
> >> > the thesis that, e.g.,
> >> >
> >> > 1-1/2-1/3+1/4-1/5 = 13/60
> >> > and
> >> > 1-1/2+1/3-1/4-1/5-1/6 = 13/60
> >> >
> >> > do not provide a counter-example...
> >> >
> >> > ;-)
> >> >
> >> > Maximilian
> >> >
> >> > _______________________________________________
> >> >
> >> > Seqfan Mailing list - http://list.seqfan.eu/
> >>
> >>
> >> _______________________________________________
> >>
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> >
> >
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> >
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>
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```