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A081564 Decimal expansion of Sum(1/(2^q-1)) with the summation extending over all pairs of integers (p,q)=1 0 < p/q < sqrt(2). 3
1, 5, 8, 0, 9, 6, 0, 3, 8, 1, 7, 1, 5, 0, 7, 0, 8, 6, 6, 8, 5, 3, 2, 5, 8, 0, 6, 5, 3, 4, 8, 8, 5, 9, 5, 0, 5, 0, 0, 3, 8, 7, 4, 2, 1, 3, 4, 6, 0, 3, 7, 5, 2, 7, 1, 0, 9, 2, 0, 5, 2, 5, 9, 2, 9, 4, 9, 9, 3, 7, 8, 3, 8, 8, 9, 6, 0, 6, 9, 4, 0, 3, 6, 8, 3, 5, 2, 7, 5, 8, 9, 1, 2, 5, 4, 6, 5, 0, 0, 1, 7, 6, 0, 8, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000

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

This sum is also equal to Sum_{k>=1} (1/2)^floor(k/sqrt(2) = 1.5809603817....

MATHEMATICA

RealDigits[ 1/(2^(1/Sqrt[2]) - 1), 10, 105] // First (* Jean-Fran├žois Alcover, Feb 15 2013 *)

PROG

(PARI) 1/(2^(1/sqrt(2)) -1) \\ G. C. Greubel, Aug 16 2018

(MAGMA) SetDefaultRealField(RealField(100)); 1/(2^(1/Sqrt(2)) -1); // G. C. Greubel, Aug 16 2018

CROSSREFS

Sequence in context: A193505 A141848 A140249 * A199073 A199069 A020797

Adjacent sequences:  A081561 A081562 A081563 * A081565 A081566 A081567

KEYWORD

cons,nonn

AUTHOR

Benoit Cloitre, Apr 21 2003

STATUS

approved

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Last modified September 19 14:43 EDT 2019. Contains 327198 sequences. (Running on oeis4.)