A265308 - OEIS

A265308

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

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, 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, 7, 0, 8, 9, 6, 0, 9, 1, 9, 7, 8, 5, 3, 3, 5, 7, 2, 7

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OFFSET

1,3

LINKS

Table of n, a(n) for n=1..86.

EXAMPLE

sum = 1.0881628951926320258095299765374284161730153...

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]