A248722 Decimal expansion of Sum_{k>=1} 1/(5^k - 1).

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

Offset: 0

Author

Robert G. Wilson v, Oct 12 2014

Keywords

• nonn
• cons

Examples

			0.301733853597972457948162159393991192623009431517157720395791923318379825892...
		

Links

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

Crossrefs

Cf. A000005, A065442, A073668, A214369, A248721, A248723, A248724, A248725, A248726.

Programs

Maple

evalf( add( (1/5)^(n^2)*(1 + 2/(5^n - 1)), n = 1..12), 105); # Peter Bala, Jan 30 2022

Mathematica

x = 1/5; RealDigits[ Sum[ DivisorSigma[0, k] x^k, {k, 1000}], 10, 105][[1]] (* after an observation and the formula of Amarnath Murthy, see A073668 *)

PARI

sumpos(k=1,1/(5^k-1)) \\ M. F. Hasler, Oct 15 2014

Formula

Equals Sum_{k>=1} d(k)/5^k, where d(k) is the number of divisors of k (A000005). - Amiram Eldar, Jun 22 2020