[seqfan] Sum over tangents

Charles Greathouse charles.greathouse at case.edu
Fri Apr 26 03:34:59 CEST 2013


Often I think about 'rescuing' sequences: adding explanation for what
otherwise appears to be an inscrutable sequence. I may have come across one
such just now.

A086227 is defined as "a(n)=1/(4i)*sum( i^k*tan(k*Pi/4/n)) where 1<=k<=4n
and (k,n)=1" with no further comment. But it seems that the absolute value
of this sequence gives the class number for Q(sqrt(-4*n^2)). Is this true?
What is the connection between these definitions?

Charles Greathouse
Analyst/Programmer
Case Western Reserve University


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