A248726 Decimal expansion of Sum_{k>=1} 1/(9^k - 1).

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

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Formula

Equals Sum_{k>=1} d(k)/9^k, where d(k) is the number of divisors of k (A000005). - Amiram Eldar, Jun 22 2020

Example

0.13904511766218812935872847436908905213936264706781960955103549347967020145366...

Maple

evalf(sum(1/(9^k-1), k=1..infinity), 120) # Vaclav Kotesovec, Oct 18 2014
# second program with faster converging series
evalf( add( (1/9)^(n^2)*(1 + 2/(9^n - 1)), n = 1..10), 105); # Peter Bala, Jan 30 2022

Mathematica

x = 1/9; RealDigits[ Sum[ DivisorSigma[0, k] x^k, {k, 1000}], 10, 105][[1]] (* after an observation and the formula of Amarnath Murthy, see A073668 *)

Prog

(PARI) suminf(k=1, 1/(9^k-1)) \\ Michel Marcus, Oct 18 2014

Crossrefs

Cf. A000005, A065442, A073668, A214369, A248721, A248722, A248723, A248724, A248725.

Sequence in context: A126321 A335777 A358945 * A267411 A370468 A021260

Adjacent sequences: A248723 A248724 A248725 * A248727 A248728 A248729

Keyword

nonn,cons

Author

Robert G. Wilson v, Oct 12 2014

Status

approved