[seqfan] Happy π Day

Bob Lyons boblyonsnj at gmail.com
Mon Mar 14 12:09:37 CET 2016


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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