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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.

%I A081550 #23 May 25 2023 11:45:48
%S A081550 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,
%T A081550 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,
%U A081550 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
%N 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.
%H A081550 Kevin O'Bryant, <a href="https://doi.org/10.1006/jnth.2001.2743">A generating function technique for Beatty sequences and other step sequences</a>, Journal of Number Theory, Volume 94, Issue 2, June 2002, Pages 299-319.
%F A081550 Equals Sum_{k>=1} (1/2)^floor(k/Pi) = Sum_{k>=1} 1/2^A032615(k).
%e A081550 6.007874015...
%t A081550 With[{digmax = 120}, RealDigits[Sum[1/2^Floor[k/Pi], {k, 1, 20*digmax}], 10, digmax][[1]]] (* _Amiram Eldar_, May 25 2023 *)
%Y A081550 Cf. A000796 (Pi).
%Y A081550 Cf. A081544, A081564, A081573.
%K A081550 cons,nonn
%O A081550 1,1
%A A081550 _Benoit Cloitre_, Apr 21 2003
%E A081550 Data corrected by _Amiram Eldar_, May 25 2023