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 A269995 Denominators of r-Egyptian fraction expansion for sqrt(2) - 1, where r = (1,1/2,1/3,1/4,...) 2
 3, 7, 36, 1300, 2206054, 14887222782418, 292542996759533035472424790, 7282957087563143077864043818232331102110274520711753058, 259880230781524461939787525796521055875618560291171401151227648777033604862236784108033156713828890456025177451 (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..12 Eric Weisstein's World of Mathematics, Egyptian Fraction EXAMPLE sqrt(2) - 1 = 1/(2*3) + 1/(3*7) + 1/(4*36) + ... 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[2] - 1; Table[n[x, k], {k, 1, z}] CROSSREFS Cf. A269993. Sequence in context: A100377 A270396 A167169 * A281093 A199347 A252795 Adjacent sequences:  A269992 A269993 A269994 * A269996 A269997 A269998 KEYWORD nonn,frac,easy AUTHOR Clark Kimberling, Mar 15 2016 STATUS approved

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Last modified January 19 06:37 EST 2020. Contains 331033 sequences. (Running on oeis4.)