[seqfan] Re: Wrong terms or wrong name in A046988?
Frank Adams-Watters
franktaw at netscape.net
Sat Mar 4 06:53:10 CET 2017
It is far more likely that there is a rounding error in the program being used for one of these definitions than that these are actually different. Without looking at the programs, that zeta(2*n)/Pi^(2*n) looks like a good candidate for an error of that sort.
Franklin T. Adams-Watters
-----Original Message-----
From: Vladimir Reshetnikov <v.reshetnikov at gmail.com>
To: seqfan <seqfan at seqfan.eu>
Cc: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Sent: Fri, Mar 3, 2017 11:25 pm
Subject: [seqfan] Wrong terms or wrong name in A046988?
Dear SeqFans,The name of the sequence A046988 contains two definitions:
"Numerators of Taylor series expansion of log(x/sin(x)).
For n>0, numerators of zeta(2*n)/Pi^(2*n)."
Presumably, it was intended that these definitions are consistent. But they
are not.The first definition results in the sequence:
1, 1, 1, 1, 1, 691, 2, 3617,43867, 174611, 155366, 236364091, 1315862, 3392780147, 6892673020804,7709321041217, 151628697551, 26315271553053477373, 308420411983322,261082718496449122051, 3040195287836141605382, 2530297234481911294093, ...
And the second: 1, 1, 1, 1, 1, 691, 2, 3617, 43867, 174611, 155366,236364091, 1315862, 6785560294, 6892673020804, 7709321041217,151628697551, 26315271553053477373, 308420411983322,261082718496449122051, 3040195287836141605382, 5060594468963822588186, ...
These sequences are similar, but disagree at indexes 14, 22, 26, 28, 30,38, 42, 44, 46, 50, 52, 54, 56, 58, 60, 62, 70, 74, 76, 78, 82, 84, 86,88, 90, 92, 94, 98, 100, ...
The terms listed in A046988 agree with the second definition. Should we
remove the first part of the name in A046988, and submit is as a new
sequence? What should we do with the leading 0 term?
--ThanksVladimir
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