The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A270356 Denominators of r-Egyptian fraction expansion for log(2), where r = (1, 1/2, 1/4, 1/8, ...) 1
 2, 3, 10, 85, 6297, 105324757, 10291333539500676, 72129634294824118806681649563665, 3614136206345221874912341551952565198060297016360952863886217259 (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 Index entries for sequences related to Egyptian fractions EXAMPLE log(2) = 1/2 + 1/(2*3) + 1/(4*10) + ... MATHEMATICA r[k_] := 2/2^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}] PROG (PARI) r(k) = 2/2^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 18 2016 CROSSREFS Cf. A269993. Sequence in context: A291935 A088222 A184249 * A333332 A229220 A155148 Adjacent sequences: A270353 A270354 A270355 * A270357 A270358 A270359 KEYWORD nonn,frac,easy AUTHOR Clark Kimberling, Mar 17 2016 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 4 13:31 EDT 2024. Contains 374921 sequences. (Running on oeis4.)