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A278386 Decimal expansion of the excess of the exponential curve arc length over the length of the x-axis from -infinity to zero. 2
2, 2, 5, 9, 8, 7, 1, 5, 5, 9, 1, 3, 4, 9, 7, 3, 3, 2, 9, 8, 6, 3, 1, 1, 5, 2, 0, 6, 8, 8, 0, 8, 2, 3, 3, 7, 6, 1, 7, 0, 1, 1, 6, 8, 1, 4, 7, 5, 5, 6, 7, 9, 1, 6, 5, 4, 4, 0, 6, 4, 1, 3, 8, 8, 3, 0, 7, 4, 8, 9, 1, 6, 2, 0, 9, 7, 7, 5, 6, 6, 6, 6, 2, 2, 5, 4, 3, 9, 6, 9, 4, 1, 3, 8, 0, 4, 2, 1, 7, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..99.

Jean-François Alcover, Involute of the exponential curve (left branch).

FORMULA

Integral_{-infinity..0} (sqrt(1 + exp(2x))-1) dx.

Equals sqrt(2) - 1 + log(2) - log(1 + sqrt(2)).

EXAMPLE

0.22598715591349733298631152068808233761701168147556791654406413883...

MATHEMATICA

RealDigits[Sqrt[2] - 1 + Log[2] - Log[1 + Sqrt[2]], 10, 100][[1]]

PROG

(PARI) sqrt(2) - 1 + log(2) - log(1 + sqrt(2)) \\ Michel Marcus, Nov 20 2016

CROSSREFS

Cf. A222362 (a similar constant).

Sequence in context: A233073 A275266 A223387 * A262614 A184296 A131133

Adjacent sequences:  A278383 A278384 A278385 * A278387 A278388 A278389

KEYWORD

nonn,cons

AUTHOR

Jean-François Alcover, Nov 20 2016

STATUS

approved

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Last modified May 28 12:26 EDT 2017. Contains 287241 sequences.