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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... .

%I A081573 #26 May 25 2023 11:40:43
%S A081573 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,
%T A081573 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,
%U A081573 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
%N 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... .
%H A081573 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 A081573 Equals Sum_{k>=1} (1/2)^floor(k/e) = Sum_{k>=1} 1/2^A032634(k).
%e A081573 4.866141732...
%t A081573 With[{digmax = 120}, RealDigits[Sum[1/2^Floor[k/E], {k, 1, 20*digmax}], 10, digmax][[1]]] (* _Amiram Eldar_, May 25 2023 *)
%Y A081573 Cf. A001113 (e).
%Y A081573 Cf. A081544, A081550, A081564.
%K A081573 cons,nonn
%O A081573 1,1
%A A081573 _Benoit Cloitre_, Apr 21 2003
%E A081573 Data corrected by _Amiram Eldar_, May 25 2023