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

Peter Lawrence peterl95124 at sbcglobal.net
Sat Mar 19 07:19:33 CET 2016


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 ¹ 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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