A081544 Decimal expansion of Sum_(1/(2^q-1)) with the summation extending over all pairs of integers gcd(p,q) = 1, 0 < p/q < phi, where phi is the Golden ratio.
2, 7, 0, 9, 8, 0, 3, 4, 4, 2, 8, 6, 1, 2, 9, 1, 3, 1, 4, 6, 4, 1, 7, 8, 7, 3, 9, 9, 4, 4, 4, 5, 7, 5, 5, 9, 7, 0, 1, 2, 5, 0, 2, 2, 0, 5, 7, 6, 7, 8, 6, 0, 5, 1, 6, 9, 5, 7, 0, 0, 2, 6, 4, 4, 6, 5, 1, 2, 8, 7, 1, 2, 8, 1, 4, 8, 4, 6, 5, 9, 6, 2, 4, 7, 8, 3, 1, 6, 1, 3, 2, 4, 5, 9, 9, 9, 3, 8, 8, 3, 9, 2, 6, 5, 3
Offset: 1
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
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Mathematica
With[{digmax = 120}, RealDigits[Sum[1/2^Floor[k/GoldenRatio], {k, 1, 10*digmax}], 10, digmax][[1]]] (* Amiram Eldar, May 25 2023 *)
Formula
Equals Sum_{k>=1} (1/2)^floor(k/phi).
Extensions
Data corrected by Amiram Eldar, May 25 2023