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 A269996 Denominators of r-Egyptian fraction expansion for sqrt(3) - 1, where r = (1,1/2,1/3,1/4,...) 2
 2, 3, 6, 26, 939, 800567, 626897816036, 732632470241183632257841, 31706715561023122142248280773186018287458544854469, 1666726692230759969765850044548001173784581299264219742879080654883940143766478552206863259848365362 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Suppose that r is a sequence of rational numbers r(k) <= 1 for k >= 1, and that x is an irrational number in (0,1).  Let f(0) = x, n(k) = floor(r(k)/f(k-1)), and f(k) = f(k-1) - r(k)/n(k).  Then x = r(1)/n(1) + r(2)/n(2) + r(3)/n(3) + ... , the r-Egyptian fraction for x. See A269993 for a guide to related sequences. LINKS Clark Kimberling, Table of n, a(n) for n = 1..13 Eric Weisstein's World of Mathematics, Egyptian Fraction EXAMPLE sqrt(3) - 1 = 1/2 + 1/(2*3) + 1/(3*6) + ... MATHEMATICA r[k_] := 1/k; f[x_, 0] = x; z = 10; n[x_, k_] := n[x, k] = Ceiling[r[k]/f[x, k - 1]] f[x_, k_] := f[x, k] = f[x, k - 1] - r[k]/n[x, k] x = Sqrt[3] - 1; Table[n[x, k], {k, 1, z}] CROSSREFS Cf. A269993. Sequence in context: A144857 A090445 A228346 * A336240 A336458 A348867 Adjacent sequences:  A269993 A269994 A269995 * A269997 A269998 A269999 KEYWORD nonn,frac,easy AUTHOR Clark Kimberling, Mar 15 2016 STATUS approved

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Last modified May 21 07:22 EDT 2022. Contains 353889 sequences. (Running on oeis4.)