A372858 Decimal expansion of (1 + log(2))/2.

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

Offset

0,1

Links

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

Formula

Equals Integral_{x=2..oo} (log(x))/x^2 dx.

Equals log(A019798). - Hugo Pfoertner, Jun 09 2024

Integral log(x)/x^m dx = -x^(1-m) Sum_{k=0..1} log^(1-k)(x)/(m-1)^(k+1). - R. J. Mathar, Jun 21 2024

Example

0.84657359027997265470861606072908828403775006...

Mathematica

s = Integrate[Log[x]/x^2, {x, 2, Infinity}]
d = N[s, 100]
First[RealDigits[d]]
N[1/2  (1 + Log[2]), 100]

Crossrefs

Cf. A019798, A372859, A372860, A372861.

Essentially the same as A016655, A102047.

Sequence in context: A092727 A020842 A255987 * A266556 A199434 A253073

Adjacent sequences: A372854 A372856 A372857 * A372859 A372864 A372865

Keyword

nonn,cons,new

Author

Clark Kimberling, Jun 09 2024

Status

approved