a(n) = Sum_{k=1..n} [ 1/{k*sqrt(7)} ] where {x} := x - [ x ].

Terms

a(0) =1a(1) =4a(2) =5a(3) =6a(4) =10a(5) =11a(6) =12a(7) =18a(8) =19a(9) =21a(10) =30a(11) =31a(12) =33a(13) =57a(14) =58a(15) =61a(16) =62a(17) =63a(18) =66a(19) =67a(20) =68a(21) =72a(22) =73a(23) =75a(24) =81a(25) =82a(26) =84a(27) =96a(28) =97a(29) =99