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 A265299 Decimal expansion of sum{c(2n) - c(2n-1), n=1,2,...}, where c = convergents to (x = sqrt(5)). 4
 2, 5, 0, 8, 1, 9, 5, 3, 9, 0, 5, 4, 3, 0, 8, 8, 8, 2, 2, 2, 5, 8, 1, 2, 1, 1, 5, 2, 5, 8, 3, 7, 0, 4, 7, 6, 1, 1, 4, 7, 8, 0, 6, 7, 5, 8, 2, 4, 5, 8, 8, 7, 8, 0, 8, 0, 7, 0, 3, 1, 8, 0, 1, 6, 1, 2, 1, 0, 5, 9, 5, 6, 9, 1, 4, 2, 4, 6, 2, 2, 9, 0, 8, 4, 6, 5 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS EXAMPLE sum = 0.25081953905430888222581211525837047611... MATHEMATICA x = Sqrt[5]; 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]]  (* A265297 *) RealDigits[s2, 10, 120][[1]]  (* A265298 *) RealDigits[s1 + s2, 10, 120][[1]](* A265299 *) CROSSREFS Cf. A002163, A265297, A265298, A265288 (guide). Sequence in context: A022832 A008348 A201576 * A020836 A111466 A308715 Adjacent sequences:  A265296 A265297 A265298 * A265300 A265301 A265302 KEYWORD nonn,cons AUTHOR Clark Kimberling, Dec 07 2015 STATUS approved

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Last modified August 1 18:47 EDT 2021. Contains 346402 sequences. (Running on oeis4.)