cp's OEIS Frontend

A265307 Decimal expansion of Sum_{k>=1} (c(2k)-e), where c = convergents to e.

%I A265307 #8 Dec 20 2015 13:48:46
%S A265307 3,1,3,9,3,4,3,0,5,9,8,4,4,1,2,4,0,5,2,5,6,5,9,6,0,0,7,5,9,6,8,3,4,7,
%T A265307 7,7,8,0,0,5,7,7,7,4,9,1,4,9,6,7,1,5,1,9,5,1,3,3,1,0,1,9,7,5,8,6,6,3,
%U A265307 8,0,2,9,1,0,5,2,2,5,2,8,5,1,6,4,1,5
%N A265307 Decimal expansion of Sum_{k>=1} (c(2k)-e), where c = convergents to e.
%e A265307 sum = 0.3139343059844124052565960075968347778005777...
%t A265307 x = E; z = 600; c = Convergents[x, z];
%t A265307 s1 = Sum[x - c[[2 k - 1]], {k, 1, z/2}]; N[s1, 200]
%t A265307 s2 = Sum[c[[2 k]] - x, {k, 1, z/2}]; N[s2, 200]
%t A265307 N[s1 + s2, 200]
%t A265307 RealDigits[s1, 10, 120][[1]]  (* A265306 *)
%t A265307 RealDigits[s2, 10, 120][[1]]  (* A265307 *)
%t A265307 RealDigits[s1 + s2, 10, 120][[1]](* A265308 *)
%Y A265307 Cf. A001113, A265306, A265308, A265288 (guide).
%K A265307 nonn,cons
%O A265307 0,1
%A A265307 _Clark Kimberling_, Dec 13 2015