[seqfan] Re: Surely not new?

Max Alekseyev maxale at gmail.com
Wed Feb 26 17:57:43 CET 2014


Hi Richard,

You miscalculated the 5th term, which should be 33/85 not 35/89. But
still the sequences are not in the OEIS.
Here is my PARI/GP one-liner for first 20 terms:

? apply(abs,contfracpnqn(vector(20,n,(-1)^(n-1)*n),20))
%1 =
[1 1 1 2 7 33 191 1304 10241 90865 898409 9791634 116601199 1506023953
20967734143 313009988192 4987192076929 84469255319601 1515459403675889
28709259414522290 572669728886769911]

[0 1 2 5 18 85 492 3359 26380 234061 2314230 25222469 300355398
3879397705 54011212472 806288789375 12846609417528 217586071308601
3903702674137290 73952764737299909 1475151592071860890]

Regards,
Max

On Wed, Feb 26, 2014 at 11:40 AM, rkg <rkg at cpsc.ucalgary.ca> wrote:
> Sorry if this is well known to those who well know it, but the following
> seem not to be in OEIS:
>
> 1, 1, 2,  7, 35, 191, 1304, ...
> 1, 2, 5, 18, 89, 492, 3359, ...
>
> Presumably because I've made a stupid mistake in my hand clculations.
>
> They are the numerators and denominators of the convergents to
> the negative continued fraction 1 - 1/(2 - 1/(3 - 1/(4 - ...)))  R.
>
>
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