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 A322711 Decimal expansion of the sum of reciprocals of the products of 9 consecutive Fibonacci numbers. 3
 4, 5, 7, 1, 5, 2, 2, 7, 6, 2, 0, 6, 4, 8, 1, 8, 3, 7, 2, 5, 9, 8, 4, 4, 5, 5, 7, 2, 8, 8, 9, 5, 1, 8, 5, 4, 9, 1, 1, 3, 7, 2, 6, 0, 1, 2, 5, 5, 7, 9, 3, 8, 1, 5, 8, 9, 6, 0, 7, 5, 1, 7, 8, 7, 0, 5, 4, 0, 1, 1, 3, 3, 3, 7, 6, 6, 7, 8, 6, 3, 4, 2, 1, 2, 1, 9, 5 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET -6,1 LINKS Robert G. Wilson v, Table of n, a(n) for n = -6..10000 Brother Alfred Brousseau, Summation of Infinite Fibonacci Series, The Fibonacci Quarterly, Vol. 7, No. 2 (1969), pp. 143-168. See (23) p. 167. Stanley Rabinowitz, Algorithmic summation of reciprocals of products of Fibonacci numbers, The Fibonacci Quarterly, Vol. 37 (1999), pp. 122-127, alternative link. See (29) p. 127 or p. 7. FORMULA Equals to (319/16380) * (Sum_{k>=1} 1/F(k) - 46816051/13933920), where F(k) is the k-th Fibonacci number. EXAMPLE 4.57152276206481837259844557288951854911372601255793... * 10^(-7). MATHEMATICA digits = 100; f[n_] := Product[Fibonacci[k], {k, n, n+8}]; NSum[1/f[n], {n, 1, Infinity}, WorkingPrecision -> digits, NSumTerms -> digits] // RealDigits[#, 10, digits] & // First (* after Jean-François Alcover at A079586 *) RealDigits[ Sum[ N[ 1/Product[ Fibonacci@j, {j, k, k + 8}], 128], {k, 59}], 10, 111][[1]] (* Robert G. Wilson v, Feb 11 2019 *) CROSSREFS Cf. A000045, A079586, A290565. Sequence in context: A112247 A319260 A237196 * A057055 A177883 A245422 Adjacent sequences:  A322708 A322709 A322710 * A322712 A322713 A322714 KEYWORD nonn,cons AUTHOR Amiram Eldar, Dec 24 2018 STATUS approved

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Last modified June 2 11:35 EDT 2020. Contains 334771 sequences. (Running on oeis4.)