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 A270557 Denominators of r-Egyptian fraction expansion for (1/2)^(1/3), where r(k) = 1/(2k-1). 2
 2, 2, 2, 6, 35, 1828, 87102089, 9369260399911997, 79759690931475868535017424372273, 6278545782421133501164266118042557416295332543123744442037840298 (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 (1/2)^(1/3) = 1/(1*2) + 1/(3*2) + 1/(5*2) + 1/(7*6) + ... MATHEMATICA r[k_] := 1/(2k-1); 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 = (1/2)^(1/3); Table[n[x, k], {k, 1, z}] CROSSREFS Cf. A269993, A005408. Sequence in context: A321741 A101416 A098920 * A129365 A125838 A021453 Adjacent sequences:  A270554 A270555 A270556 * A270558 A270559 A270560 KEYWORD nonn,frac,easy AUTHOR Clark Kimberling, Apr 03 2016 STATUS approved

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Last modified October 21 14:58 EDT 2019. Contains 328301 sequences. (Running on oeis4.)