A081573 Decimal expansion of Sum_(1/(2^q-1)) with the summation extending over all pairs of integers gcd(p,q) = 1, 0 < p/q < e = 2.718... .
4, 8, 6, 6, 1, 4, 1, 7, 3, 2, 2, 8, 5, 2, 9, 7, 8, 7, 9, 0, 8, 3, 8, 9, 2, 0, 7, 2, 0, 1, 0, 8, 6, 5, 9, 5, 0, 8, 4, 8, 6, 8, 2, 5, 7, 4, 5, 4, 4, 0, 3, 3, 2, 2, 6, 4, 7, 5, 5, 1, 3, 5, 4, 1, 0, 8, 3, 3, 3, 3, 8, 4, 7, 0, 4, 6, 0, 1, 0, 2, 4, 4, 0, 4, 8, 5, 9, 5, 9, 1, 1, 2, 9, 5, 5, 2, 7, 8, 0, 8, 0, 0, 0, 5, 5
Offset: 1
Examples
4.866141732...
Links
- Kevin O'Bryant, A generating function technique for Beatty sequences and other step sequences, Journal of Number Theory, Volume 94, Issue 2, June 2002, Pages 299-319.
Programs
-
Mathematica
With[{digmax = 120}, RealDigits[Sum[1/2^Floor[k/E], {k, 1, 20*digmax}], 10, digmax][[1]]] (* Amiram Eldar, May 25 2023 *)
Formula
Equals Sum_{k>=1} (1/2)^floor(k/e) = Sum_{k>=1} 1/2^A032634(k).
Extensions
Data corrected by Amiram Eldar, May 25 2023