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 A270485 Denominators of r-Egyptian fraction expansion for log(2), where r(k) = 1/Prime(k). 1
 1, 2, 8, 97, 11716, 172250929, 464527945899982923, 716536589150920535839270312752276315, 459309301489561677977334026730028085729138984938021544486509797638182462 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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 log(2) = 1/(2*1) + 1/(3*2) + 1/(5*8) + 1/(7*97) + ... MATHEMATICA r[k_] := 1/Prime[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[2]; Table[n[x, k], {k, 1, z}] CROSSREFS Cf. A269993, A000040. Sequence in context: A326866 A001697 A006069 * A223042 A052457 A119654 Adjacent sequences:  A270482 A270483 A270484 * A270486 A270487 A270488 KEYWORD nonn,frac,easy AUTHOR Clark Kimberling, Mar 30 2016 STATUS approved

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Last modified May 27 21:52 EDT 2020. Contains 334671 sequences. (Running on oeis4.)