A332632 Decimal expansion of arclength between (0,1) and (1,1/2) on y = 1/2^x.

1, 1, 2, 1, 5, 5, 3, 1, 8, 2, 4, 0, 0, 7, 3, 6, 0, 3, 1, 2, 0, 8, 1, 8, 5, 7, 1, 7, 1, 4, 4, 7, 9, 3, 7, 5, 2, 6, 2, 4, 5, 2, 5, 5, 1, 6, 6, 7, 0, 5, 0, 8, 8, 5, 4, 7, 8, 5, 0, 2, 3, 3, 8, 8, 2, 7, 9, 0, 1, 5, 9, 7, 1, 7, 7, 5, 6, 0, 8, 4, 0, 6, 4, 5, 2, 3

Offset

1,3

Links

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

Formula

Equals (sqrt(1+log(2)^2) - sqrt(1+(log(2)/2)^2) + arcsinh(2/log(2)) - arcsinh(1/log(2)))/log(2). - Amiram Eldar, May 16 2026

Example

1.1215531824007360312081857171447937526245255166...

Mathematica

s = Integrate[Sqrt[1 + D[2^(-x), x]^2], {x, 0, 1}]
r = N[s, 200]
RealDigits[r][[1]]

Crossrefs

Cf. A333202, A332630.

Sequence in context: A108410 A058116 A058118 * A124226 A248797 A193536

Adjacent sequences: A332629 A332630 A332631 * A332633 A332634 A332635

Keyword

nonn,cons,easy

Author

Clark Kimberling, Jun 12 2020

Status

approved