A374641 Decimal expansion of log(9/10), negated.

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

Offset

0,3

Comments

Bailey et al. (1997) use Li_1(1/10) (see Formula section) to compute the ten billionth digit of this constant.

Bailey and Crandall (2001), p. 185, present this constant as an example of an irrational number that, provided their "Hypothesis A" (p. 176) is true, is normal to base 10.

Also decimal expansion of log(10/9). - Charles R Greathouse IV, Jul 17 2024

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

David Bailey, Peter Borwein, and Simon Plouffe, On the Rapid Computation of Various Polylogarithmic Constants, Mathematics of Computation, Vol. 66, No. 218, April 1997, pp. 903-913.

David H. Bailey and Richard E. Crandall, On the Random Character of Fundamental Constant Expansions, Experimental Mathematics, Vol. 10 (2001), Issue 2, pp. 175-190 (preprint draft).

Eric Weisstein's MathWorld, Polylogarithm.

Wikipedia, Polylogarithm.

Formula

Equals Li_1(1/10) = Sum_{k >= 1} 1/(k*10^k), where Li_m(z) is the polylogarithm function. See Bailey et al. (1997), p. 909 and Bailey and Crandall (2001), p. 185.

Example

0.105360515657826301227500980839312798306120372983...

Mathematica

First[RealDigits[Log[9/10], 10, 100]]

Prog

(PARI) -log(.9) \\ Charles R Greathouse IV, Jul 17 2024

Crossrefs

Cf. A126431, A374642, A374643, A374644.

Sequence in context: A073685 A019212 A374642 * A201928 A021655 A360270

Adjacent sequences: A374638 A374639 A374640 * A374642 A374643 A374644

Keyword

nonn,cons

Author

Paolo Xausa, Jul 15 2024

Status

approved