A367409 Decimal expansion of arclength of (1 - 2^(1-x)) zeta(x), for 0 < x < 1.

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

Offset

1,4

Comments

See A367309.

Links

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

Example

1.0186563516740513673662299252527545340266...

Mathematica

f[x_] := (1 - 2^(1 - x)) Zeta[x]
y = NIntegrate[Sqrt[1 + f'[x]^2], {x, 0, 1}, WorkingPrecision -> 200]
RealDigits[y][[1]]

Prog

(PARI) f(x) = (1 - 2^(1-x))*zeta(x); intnum(x=0, 1, sqrt(1+f'(x)^2)) \\ Michel Marcus, Nov 27 2023

Crossrefs

Cf. A113024, A367309, A367311.

Sequence in context: A120818 A125579 A202258 * A021540 A100199 A161883

Adjacent sequences: A367406 A367407 A367408 * A367410 A367411 A367412

Keyword

nonn,cons

Author

Clark Kimberling, Nov 26 2023

Status

approved