[seqfan] Re: Reciprocal Recaman
M. F. Hasler
oeis at hasler.fr
Sun Nov 17 00:10:45 CET 2013
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
>> >
>> > _______________________________________________
>> >
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>>
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