login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A270002 Denominators of r-Egyptian fraction expansion for e - 2, where r = (1,1/2,1/3,1/4,...) 2
2, 3, 7, 63, 7179, 142233093, 64600110035609517, 5529148350206824361693538422450743, 39876890198849678230595649918157265458164953427845442505533508344048 (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

e - 2 = 1/2 + 1/(2*3) + 1/(3*7) + ...

MATHEMATICA

r[k_] := 1/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 = E - 2; Table[n[x, k], {k, 1, z}]

CROSSREFS

Cf. A269993.

Sequence in context: A299923 A087358 A255357 * A057736 A181263 A130309

Adjacent sequences:  A269999 A270000 A270001 * A270003 A270004 A270005

KEYWORD

nonn,frac,easy

AUTHOR

Clark Kimberling, Mar 15 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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 19 13:25 EST 2020. Contains 332044 sequences. (Running on oeis4.)