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A265308 Decimal expansion of Sum_{k>=1} (c(2k)-c(2k-1)), where c = convergents to e.

%I A265308 #8 Dec 20 2015 13:49:38
%S A265308 1,0,8,8,1,6,2,8,9,5,1,9,2,6,3,2,0,2,5,8,0,9,5,2,9,9,7,6,5,3,7,4,2,8,
%T A265308 4,1,6,1,7,3,0,1,5,3,8,6,3,9,2,6,4,5,4,3,5,7,2,9,4,4,2,7,9,1,7,9,0,0,
%U A265308 7,0,8,9,6,0,9,1,9,7,8,5,3,3,5,7,2,7
%N A265308 Decimal expansion of Sum_{k>=1} (c(2k)-c(2k-1)), where c = convergents to e.
%e A265308 sum = 1.0881628951926320258095299765374284161730153...
%t A265308 x = E; z = 600; c = Convergents[x, z];
%t A265308 s1 = Sum[x - c[[2 k - 1]], {k, 1, z/2}]; N[s1, 200]
%t A265308 s2 = Sum[c[[2 k]] - x, {k, 1, z/2}]; N[s2, 200]
%t A265308 N[s1 + s2, 200]
%t A265308 RealDigits[s1, 10, 120][[1]]  (* A265306 *)
%t A265308 RealDigits[s2, 10, 120][[1]]  (* A265307 *)
%t A265308 RealDigits[s1 + s2, 10, 120][[1]](* A265308 *)
%Y A265308 Cf. A001113, A265306, A265307, A265288 (guide).
%K A265308 nonn,cons
%O A265308 1,3
%A A265308 _Clark Kimberling_, Dec 13 2015