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!)
 A270481 Denominators of r-Egyptian fraction expansion for 1/Pi, where r(k) = 1/Prime(k). 1
 2, 5, 122, 36864, 13343376668, 224851808819852270264, 206030526699009549783863692475305411157116, 42500635870294544529750048452464143848264977426702636517113215245943832312921983097 (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 1/Pi = 1/(2*2) + 1/(3*5) + 1/(5*122) + 1/(7*36864) + ... 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 = 1/Pi; Table[n[x, k], {k, 1, z}] CROSSREFS Cf. A269993, A000040. Sequence in context: A132526 A294513 A276109 * A225944 A270588 A214648 Adjacent sequences:  A270478 A270479 A270480 * A270482 A270483 A270484 KEYWORD nonn,frac,easy AUTHOR Clark Kimberling, Mar 30 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 June 13 17:14 EDT 2021. Contains 345008 sequences. (Running on oeis4.)