|
|
A248725
|
|
Decimal expansion of Sum_{k>=1} 1/(8^k - 1).
|
|
10
|
|
|
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
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
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
|
# 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
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|