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

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, 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, 8, 0, 2, 9, 1, 0, 5, 2, 2, 5, 2, 8, 5, 1, 6, 4, 1, 5

Offset: 0

Author

Clark Kimberling, Dec 13 2015

Keywords

• nonn
• cons

Examples

			sum = 0.3139343059844124052565960075968347778005777...
		

Crossrefs

Cf. A001113, A265306, A265308, A265288 (guide).

Programs

Mathematica

x = E; z = 600; c = Convergents[x, z];
s1 = Sum[x - c[[2 k - 1]], {k, 1, z/2}]; N[s1, 200]
s2 = Sum[c[[2 k]] - x, {k, 1, z/2}]; N[s2, 200]
N[s1 + s2, 200]
RealDigits[s1, 10, 120][[1]]  (* A265306 *)
RealDigits[s2, 10, 120][[1]]  (* A265307 *)
RealDigits[s1 + s2, 10, 120][[1]](* A265308 *)