Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #13 Jan 07 2021 21:31:35
%S 3,7,8,3,4,4,0,9,8,3,5,0,0,7,9,7,6,6,6,6,8,3,6,8,1,6,3,9,2,2,7,9,8,9,
%T 1,5,6,1,0,7,5,0,8,5,8,9,8,6,0,1,1,2,7,4,3,1,9,8,1,9,8,0,6,3,6,6,9,1,
%U 0,7,1,0,1,1,2,5,2,3,2,2,7,6,3,6,3,4,2,2,0,6,6,9,8,1,1,9,3,7,1,8,5,6,3,9
%N Decimal expansion of sum of reciprocals of A000111(n) (where A000111(n) is the n-th Euler or up/down number).
%C The series 1/1 + 1/1 + 1/1 + 1/2 + 1/5 + 1/16 + 1/61 + 1/272 + 1/1385 + 1/7936 + ... converges to 3.783440983500797666683...
%F Equals Sum_{k>=0} 1/A000111(k).
%e 3.783440983500797666683...
%o (PARI) f(n)=if(n, 2*abs(polylog(-n, I)), 1); \\ A000111
%o suminf(n=0, 1/f(n)) \\ _Michel Marcus_, Jan 04 2021
%Y Cf. A000111, A001250, A173253.
%K nonn,cons
%O 1,1
%A _Marco Ripà_, Jan 04 2021
%E More digits from _Alois P. Heinz_, Jan 06 2021