A372860 -id:A372860

Search: a372860 -id:a372860

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A372858

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

+10
3

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

(list; constant; graph; refs; listen; history; text; internal format)

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.

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Jun 09 2024

STATUS

approved

A372859

Decimal expansion of (1 + log(4))/16.

+10
3

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

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

FORMULA

Equals Integral_{x=2..oo} log(x)/x^3 dx.

EXAMPLE

0.149143397569993163677154015182272071009437516795031...

MATHEMATICA

s = Integrate[Log[x]/x^3, {x, 2, Infinity}]

d = N[s, 100]

First[RealDigits[d]]

N[1/16 (1 + Log[4]), 100]

CROSSREFS

Cf. A372858, A372860, A372861.

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Jun 09 2024

STATUS

approved

A372861

Decimal expansion of (1 + log(16))/256.

+10
3

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Table of n, a(n) for n=0..84.

FORMULA

Equals Integral_{x=2..oo} log(x)/x^5 dx.

EXAMPLE

0.0147366746962491454596442518977840088761796895993...

MATHEMATICA

s = Integrate[Log[x]/x^5, {x, 2, Infinity}]

d = N[s, 100]

Join[{0}, First[RealDigits[d]]]

N[1/256 (1 + Log[16]), 100]

CROSSREFS

Cf. A372858, A372859, A372860.

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Jun 12 2024

STATUS

approved

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