OFFSET
0,1
LINKS
Kevin Ryde, Table of n, a(n) for n = 0..10000
W. E. Greig, Sums of Fibonacci Reciprocals, The Fibonacci Quarterly, Vol. 15, No. 1, February 1977, pp. 46-48 (see equation (15)).
FORMULA
Equals Sum_{j>=1} phi^(2*j)/(phi^(4*j) - 1) [Greig, equation (15)].
Equals A153386 / sqrt(5) [Greig, equations (13) and (14)].
EXAMPLE
0.68663856568126063939655676567056596...
MATHEMATICA
RealDigits[Sum[1/(GoldenRatio^(4*i + 2) - 1), {i, 0, Infinity}], 10, 105][[1]] (* Amiram Eldar, Feb 26 2023 *)
RealDigits[(Log[(5 + 3*Sqrt[5])/2] + QPolyGamma[0, 1/2, (7 + 3*Sqrt[5])/2]) / Log[(7 - 3*Sqrt[5])/2], 10, 105][[1]] (* Vaclav Kotesovec, Feb 26 2023 *)
PROG
(PARI) sumpos(i=0, 1/(((1+sqrt(5))/2)^(4*i+2) - 1)) \\ Michel Marcus, Feb 26 2023
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Kevin Ryde, Feb 25 2023
STATUS
approved