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 A270002 Denominators of r-Egyptian fraction expansion for e - 2, where r = (1,1/2,1/3,1/4,...) 2
 2, 3, 7, 63, 7179, 142233093, 64600110035609517, 5529148350206824361693538422450743, 39876890198849678230595649918157265458164953427845442505533508344048 (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 e - 2 = 1/2 + 1/(2*3) + 1/(3*7) + ... 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 = E - 2; Table[n[x, k], {k, 1, z}] CROSSREFS Cf. A269993. Sequence in context: A299923 A087358 A255357 * A057736 A181263 A130309 Adjacent sequences:  A269999 A270000 A270001 * A270003 A270004 A270005 KEYWORD nonn,frac,easy AUTHOR Clark Kimberling, Mar 15 2016 STATUS approved

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Last modified February 19 13:25 EST 2020. Contains 332044 sequences. (Running on oeis4.)