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

1,1

Links

Table of n, a(n) for n=1..105.

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.

Formula

Equals Sum_{k>=1} (1/2)^floor(k/e) = Sum_{k>=1} 1/2^A032634(k).

Example

4.866141732...

Mathematica

With[{digmax = 120}, RealDigits[Sum[1/2^Floor[k/E], {k, 1, 20*digmax}], 10, digmax][[1]]] (* Amiram Eldar, May 25 2023 *)

Crossrefs

Cf. A001113 (e).

Cf. A081544, A081550, A081564.

Sequence in context: A198885 A336275 A177157 * A201527 A063808 A081455

Adjacent sequences: A081570 A081571 A081572 * A081574 A081575 A081576

Keyword

cons,nonn

Author

Benoit Cloitre, Apr 21 2003

Extensions

Data corrected by Amiram Eldar, May 25 2023

Status

approved