[seqfan] a curiosity, about A017979

[Simon Plouffe]

hello seqfan,

  I have this curiosity,

  The sequence A017979 when evaluated at exp(-2*Pi)
is equal to

            5/8
          2
   1/2 ----------
           23 Pi
       exp(-----)
            12

to a precision of 35 decimal digits.

That is : sum(a(n)/exp(2*Pi*n),n=1..infinity), where a(n) = A017979(n).

  Can anyone find why ?

recall : A017979, is :

%S A017979 1,1,1,2,2,3,4,5,6,8,10,12,16,20,25,32,40,50,64,80,101,
%T A017979 128,161,203,256,322,406,512,645,812,1024,1290,1625,2048,
%U A017979 2580,3250,4096,5160,6501,8192,10321,13003,16384,20642
%N A017979 Powers of cube root of 2 rounded down.

Curious isn't ?

Cheers and happy new year,

simon plouffe