[seqfan] Re: duplicate seqs?, re: Happy PI day

jean-paul allouche jean-paul.allouche at imj-prg.fr
Sat Mar 19 10:19:23 CET 2016


Dear Peter

The syntax to get the signed sequence is
"signed: 1, 1, 1, 1,-1, 1, 1, 1, 1,-1, 1, 1,-1, 1,-1, 1,-1,
1, 1,-1, 1, 1,-1, 1, 1"

Doing that with many terms of A070750 seems to show that
it differs from A209661, if I am not mistaken

best
jean-paul

Le 19/03/16 07:19, Peter Lawrence a écrit :
> Neil,
>           this PI-day post caught my interest and got me wondering
> about the sequence of "signs"
>
> first I searched " 1, 1, 1, 1,-1, 1, 1, 1, 1,-1, 1, 1,-1, 1,-1, 1,-1,
> 1, 1,-1, 1, 1,-1, 1, 1"
> but the search engine apparently ignored signs on this one
> so the sequence I was looking for was way down on the list of
> matches ???
> but I did finally locate A070750
>
> then I followed the original post's link to A209662, and from there
> to A209661,
> which near as I can tell is duplicate of A07050 (the mathematical
> definitions
> match in addition to the apparent match of the listed values)
>
>
> second I searched "1, 2, 3, 4, -5, 6, 7, 8, 9, -10, 11, 12, -13, 14
> -15, 16, -17, 18, 19, -20"
> and A209662 showed up at the top of the list rather than way down ???
>
>
> so what is the search engine doing with signs ?
>
> it would seem to be a benefit if it consistently honored user-input
> signs ?
> much like commas emphasize strict ordering ?
>
> if A070750 and A209661 are actually duplicates, a better search
> engine could have caught it ?
>
>
> --Peter Lawrence.
>
>
>
>
> >
> > ------------------------------
> >
> > Message: 21
> > Date: Mon, 14 Mar 2016 07:09:37 -0400
> > From: Bob Lyons <boblyonsnj at gmail.com>
> > To: seqfan at list.seqfan.eu
> > Subject: [seqfan] Happy π Day
> > Message-ID:
> > <CAJ=EaLRLyaY6q7_AG3ns-HYgfrXza_FFqNq6GAaWR+vJDPbLQA at mail.gmail.com>
> > Content-Type: text/plain; charset=UTF-8
> >
> > Happy
> >
> > 1 + 1/2 + 1/3 + 1/4 - 1/5 + 1/6 + 1/7 + 1/8 + 1/9 - 1/10 + 1/11 +
> > 1/12 -
> > 1/13 + ...
> >
> > Day!
> >
> >
> > Series by Euler, 1748.
> >
> > http://curiosamathematica.tumblr.com/post/79567536884/consider-the-
> > following-series-by-euler-1748
> >
> > "The first two terms get positive signs. For every other term, the
> > sign is
> > defined as follows: if the denominator is a prime of the form 4m -
> > 1, the
> > term is positive; if the denominator is a prime of the form 4m + 1,
> > the
> > term is negative; for composite numbers, the sign of the term
> > equals the
> > product of the signs of its factors."
> >
> >
> > See also https://oeis.org/A209662
> >
> >
> > Bob
> >
> >
> > ------------------------------
> >
> >
>
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/



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