A265307 - OEIS

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

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OFFSET

0,1

LINKS

Table of n, a(n) for n=0..85.

EXAMPLE

sum = 0.3139343059844124052565960075968347778005777...

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]