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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.
3
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
1,1
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.
FORMULA
Equals Sum_{k>=1} (1/2)^floor(k/phi).
Equals A014565 + 2 = A073115 + 1. - Amiram Eldar, May 25 2023
MATHEMATICA
With[{digmax = 120}, RealDigits[Sum[1/2^Floor[k/GoldenRatio], {k, 1, 10*digmax}], 10, digmax][[1]]] (* Amiram Eldar, May 25 2023 *)
CROSSREFS
Cf. A001622 (golden ratio), A014565, A073115.
Sequence in context: A016638 A199398 A296453 * A011294 A282072 A282493
KEYWORD
cons,nonn
AUTHOR
Benoit Cloitre, Apr 21 2003
EXTENSIONS
Data corrected by Amiram Eldar, May 25 2023
STATUS
approved