A248725 Decimal expansion of Sum_{k>=1} 1/(8^k - 1).

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

Offset

0,2

Links

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

Formula

Equals Sum_{k>=1} d(k)/8^k, where d(k) is the number of divisors of k (A000005). - Amiram Eldar, Jun 22 2020

Example

0.16096618431506239680530256414364288555074385602532834636083591864782394085800...

Maple

evalf(sum(1/(8^k-1), k=1..infinity), 120) # Vaclav Kotesovec, Oct 18 2014
# second program with faster converging series
evalf( add( (1/8)^(n^2)*(1 + 2/(8^n - 1)), n = 1..10), 105); # Peter Bala, Jan 30 2022

Mathematica

x = 1/8; 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/(8^k-1)) \\ Michel Marcus, Oct 18 2014

Crossrefs

Cf. A000005, A065442, A073668, A214369, A248721, A248722, A248723, A248724, A248726.

Sequence in context: A112246 A189037 A153201 * A118178 A021168 A147709

Adjacent sequences: A248722 A248723 A248724 * A248726 A248727 A248728

Keyword

nonn,cons

Author

Robert G. Wilson v, Oct 12 2014

Status

approved