The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A270348 Denominators of r-Egyptian fraction expansion for sqrt(1/3), where r = (1,1/2,1/4,1/8,...) 1
 2, 7, 43, 1161, 796510, 1101781866330, 648667164391834988511313, 521313118065995695198529265268104396429334449023, 177042477384698216444912803612486097958997328262217304760270340328784709181787835108737458616981 (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..11 Eric Weisstein's World of Mathematics, Egyptian Fraction EXAMPLE sqrt(1/3) = 1/2 + 1/(2*7) + 1/(4*43) + ... 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 = Sqrt[1/3]; 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=sqrt(1/3)) = ceil(r(k)/f(k-1, x)); \\ Michel Marcus, Mar 18 2016 CROSSREFS Cf. A269993. Sequence in context: A011835 A198946 A212270 * A270580 A103084 A041507 Adjacent sequences:  A270345 A270346 A270347 * A270349 A270350 A270351 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 18 13:34 EST 2021. Contains 340254 sequences. (Running on oeis4.)