A081550 Decimal expansion of Sum_(1/(2^q-1)) with the summation extending over all pairs of integers gcd(p,q) = 1, 0 < p/q < Pi.

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

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/Pi) = Sum_{k>=1} 1/2^A032615(k).

Example

6.007874015...

Mathematica

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

Crossrefs

Cf. A000796 (Pi).

Cf. A081544, A081564, A081573.

Sequence in context: A217219 A113555 A066604 * A252244 A019929 A368206

Adjacent sequences: A081547 A081548 A081549 * A081551 A081552 A081553

Keyword

cons,nonn

Author

Benoit Cloitre, Apr 21 2003

Extensions

Data corrected by Amiram Eldar, May 25 2023

Status

approved