The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A270372 Denominators of r-Egyptian fraction expansion for sqrt(1/3), where r = (1, 1/4, 1/9, 1/16, ...). 1
 2, 4, 8, 66, 2776, 20101656, 1227318932297655, 8216049453479522437439630860819, 474082010892842884364582298006064172482079224559365990598026496 (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 sqrt(1/3) = 1/2 + 1/(4*4) + 1/(9*2) + 1/(16*3) + 1/(25*7) + ... MATHEMATICA r[k_] := 1/k^2; 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 = Sqrt[1/3]; Table[n[x, k], {k, 1, z}] PROG r(k) = 1/k^2; f(k, x) = if (k==0, x, f(k-1, x) - r(k)/a(k, x); ); a(k, x=sqrt(1/3)) = ceil(r(k)/f(k-1, x)); \\ Michel Marcus, Mar 21 2016 CROSSREFS Cf. A269993. Sequence in context: A167182 A058345 A093843 * A018507 A018523 A261714 Adjacent sequences:  A270369 A270370 A270371 * A270373 A270374 A270375 KEYWORD nonn,frac,easy AUTHOR Clark Kimberling, Mar 20 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 9 05:17 EDT 2020. Contains 335538 sequences. (Running on oeis4.)