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A265306 Decimal expansion of Sum_{k>=1} (e-c(2k-1)), where c = convergents to e.

%I A265306 #8 Dec 18 2015 11:36:49
%S A265306 7,7,4,2,2,8,5,8,9,2,0,8,2,1,9,6,2,0,5,5,2,9,3,3,9,6,8,9,4,0,5,9,3,6,
%T A265306 3,8,3,7,2,4,3,7,6,3,7,2,4,2,9,7,3,9,1,6,2,1,6,1,3,2,5,9,4,2,0,3,4,3,
%U A265306 2,8,6,6,9,8,6,7,5,3,2,4,8,4,0,8,6,3
%N A265306 Decimal expansion of Sum_{k>=1} (e-c(2k-1)), where c = convergents to e.
%e A265306 sum = 0.77422858920821962055293396894059363837243763724297...
%t A265306 x = E; z = 600; c = Convergents[x, z];
%t A265306 s1 = Sum[x - c[[2 k - 1]], {k, 1, z/2}]; N[s1, 200]
%t A265306 s2 = Sum[c[[2 k]] - x, {k, 1, z/2}]; N[s2, 200]
%t A265306 N[s1 + s2, 200]
%t A265306 RealDigits[s1, 10, 120][[1]]  (* A265306 *)
%t A265306 RealDigits[s2, 10, 120][[1]]  (* A265307 *)
%t A265306 RealDigits[s1 + s2, 10, 120][[1]](* A265308 *)
%Y A265306 Cf. A001113, A265306, A265307, A265288 (guide).
%K A265306 nonn,cons
%O A265306 0,1
%A A265306 _Clark Kimberling_, Dec 13 2015