A369884 Decimal expansion of - Integral_{x=0..1} log(1 - x)/(x^2 + x) dx.

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

Offset

1,3

Links

Table of n, a(n) for n=1..107.

Michael Ian Shamos, A catalog of the real numbers (2011), p. 110.

Eric Weisstein's World of Mathematics, Harmonic Number

Wikipedia, Harmonic number.

Formula

Equals - Integral_{x=0..1} log(1 - x)/(x^2 + x) dx.

Equals Pi^2/12 + log(2)^2/2 [Shamos].

Equals Sum_{k=>1} H(k)^2/2^(k + 1), where H(k) is the k-th Harmonic number [Shamos].

Equals (Pi^2/6 + log(2)^2)/2 = A348373/2

Example

1.062693540383213930569758846486345080474751426...

Mathematica

RealDigits[Pi^2/12 + Log[2]^2/2, 10, 120][[1]] (* Amiram Eldar, Feb 04 2024 *)

Prog

(PARI) - intnum(x=0, 1, log(1-x)/(x^2+x))

Crossrefs

Cf. A000796, A002162, A001008, A002805, A348373.

Sequence in context: A278146 A221716 A346835 * A195474 A021945 A002371

Adjacent sequences: A369881 A369882 A369883 * A369885 A369886 A369887

Keyword

nonn,cons

Author

Claude H. R. Dequatre, Feb 04 2024

Status

approved