[seqfan] Re: duplicate seqs?, re: Happy PI day
Frank Adams-Watters
franktaw at netscape.net
Sat Mar 19 09:14:30 CET 2016
First, the strategy is to look for matches including the signs first, and then for matches ignoring the signs. (Actually, I'm pretty sure it's all done in one pass, but that's the effect.)
The first match returned for your search, A011616, does in fact match the search string exactly - but this is almost certainly a false match.
A070750, however, does not. From the very beginning: I don't see 4 consecutive 1's anywhere in that sequence. Nor does its definition look anything like what you want. (Don't be misled by primes = 1 (mod 4) appearing there; the definitions are otherwise entirely different.)
A209661 was not returned as an (early) match to your query, because you were looking for a(23) = -1, while A209661 correctly has a(23) = 1.
If you are sure of your signs, you can precede the list with "signed:". This would have gotten you only A011616 in this case, because your search was wrong.
When a search doesn't turn up what you expected to find, the first thing to do is make sure that your search string is correct. I've made mistakes with that many times.
Franklin T. Adams-Watters
-----Original Message-----
From: Peter Lawrence <peterl95124 at sbcglobal.net>
To: seqfan <seqfan at list.seqfan.eu>
Sent: Sat, Mar 19, 2016 1:15 am
Subject: [seqfan] duplicate seqs?, re: Happy PI day
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
>
>
> ------------------------------
>
>
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