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 A265291 Decimal expansion of Sum_{n >= 1} (x - c(2n-1)), where c(n) = the n-th convergent to x = sqrt(2). 4
 4, 2, 8, 8, 6, 0, 3, 3, 8, 0, 6, 8, 0, 9, 5, 9, 8, 3, 0, 0, 2, 1, 1, 1, 3, 6, 7, 6, 1, 3, 2, 7, 2, 3, 0, 7, 2, 3, 9, 6, 0, 1, 7, 6, 5, 1, 2, 5, 6, 0, 8, 2, 7, 4, 6, 6, 8, 3, 0, 2, 9, 6, 0, 2, 2, 3, 0, 5, 6, 9, 3, 1, 3, 7, 0, 6, 6, 5, 3, 5, 8, 8, 2, 6, 1, 4 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS FORMULA From Peter Bala, Aug 20 2022: (Start) Equals Sum_{n >= 1} (-1)^(n+1)/Pell(2*n), where Pell(n) = A000129(n). Equals 2*sqrt(2)*Sum_{n >= 1} x^(n*(n+1)/2)/(x^n - 1), where x = 2^sqrt(2) - 3. (End) EXAMPLE sum = 0.4288603380680959830021113676132723... MAPLE x := 2*sqrt(2) - 3: evalf(2*sqrt(2)*add( x^(n*(n+1)/2)/(x^n - 1), n = 1..16), 100); # Peter Bala, Aug 21 2022 MATHEMATICA x = Sqrt[2]; z = 600; c = Convergents[x, z]; s1 = Sum[x - c[[2 k - 1]], {k, 1, z/2}]; N[s1, 200] s2 = Sum[c[[2 k]] - x, {k, 1, z/2}]; N[s2, 200] N[s1 + s2, 200] RealDigits[s1, 10, 120][[1]] (* A265291 *) RealDigits[s2, 10, 120][[1]] (* A265292 *) RealDigits[s1 + s2, 10, 120][[1]](* A265293 *) CROSSREFS Cf. A000129, A001227, A002193, A265292, A265293, A265288 (guide). Sequence in context: A197016 A198145 A143942 * A195777 A125065 A109816 Adjacent sequences: A265288 A265289 A265290 * A265292 A265293 A265294 KEYWORD nonn,cons AUTHOR Clark Kimberling, Dec 06 2015 STATUS approved

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Last modified April 1 05:25 EDT 2023. Contains 361673 sequences. (Running on oeis4.)