Sum of the reciprocals of Catalan numbers (A000108).
2, 8, 0, 6, 1, 3, 3, 0, 5, 0, 7, 7, 0, 7, 6, 3, 4, 8, 9, 1, 5, 2, 9, 2, 3, 6, 7, 0, 0, 6, 3, 1, 8, 0, 3, 2, 5, 4, 5, 9, 5, 8, 4, 9, 9, 9, 1, 5, 2, 3, 2, 9, 1, 4, 4, 6, 9, 7, 7, 2, 6, 6, 3, 7, 9, 5, 0, 2, 7, 6, 9, 6, 9, 3, 8, 9, 4, 9, 0, 6, 1, 4, 9, 7, 0, 7, 2, 2, 2, 1, 6, 9, 8, 3, 1, 3, 7, 8, 5, 2, 8, 2, 4, 9, 8, 7, 7
1
This sequence corrects A121839, which starts with 1. Koshy and Gao derive the formula for the sum.
T. D. Noe, Plot of 1001 terms
T. D. Noe, Table of 1001 terms
Thomas Koshy and Zhenguang Gao, Convergence of a Catalan Series, Vol. 43, No. 2, March 2012, The College Mathematics Journal
Wikipedia, Catalan number
The number is 2.806133050770763489152923670063180325459584999152329….
(Mma) RealDigits[2 + 4*Sqrt[3]*Pi/27, 10, 101][[1]]
Cf. A000108, A121839, S000214-S000216.
nonn,cons
T. D. Noe, Aug 26 2014