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 A270525 Denominators of r-Egyptian fraction expansion for log(2), where r(k) = 1/k!. 1
 2, 3, 7, 16, 125, 8861, 22953346, 75396230717172, 12599316539774886331286770578, 16091945901447902466261129483788815818314990863881046593, 148472040746053348386996212070544963774172473939368496909380855505454576714141628510687134372727919512688601726 (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 log(2) = 1/(1*2) + 1/(2*3) + 1/(6*7) + 1/(24*16) + ... 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 = Log; Table[n[x, k], {k, 1, z}] PROG (PARI) r(k) = 1/k!; f(k, x) = if (k==0, x, f(k-1, x) - r(k)/a(k, x); ); a(k, x=log(2)) = ceil(r(k)/f(k-1, x)); \\ Michel Marcus, Mar 31 2016 CROSSREFS Cf. A269993, A000142, A002162. Sequence in context: A036356 A034732 A000278 * A153787 A141795 A077322 Adjacent sequences:  A270522 A270523 A270524 * A270526 A270527 A270528 KEYWORD nonn,frac,easy AUTHOR Clark Kimberling, Mar 30 2016 STATUS approved

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Last modified March 25 22:28 EDT 2019. Contains 321477 sequences. (Running on oeis4.)