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A270354 Denominators of r-Egyptian fraction expansion for 1/e, where r = (1, 1/2, 1/4, 1/8, ...) 1
3, 15, 207, 24777, 1797835772, 2401072239422894903, 36947191921380265723491992928675837908, 1242004943621920150072266455052958650167034792376067355585774287542963919184 (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

Index entries for sequences related to Egyptian fractions

EXAMPLE

1/e = 1/3 + 1/(2*15) + 1/(4*207) + ...

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 = 1/E; 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=exp(-1)) = ceil(r(k)/f(k-1, x)); \\ Michel Marcus, Mar 18 2016

CROSSREFS

Cf. A269993.

Sequence in context: A166359 A195515 A003505 * A120601 A145272 A264705

Adjacent sequences:  A270351 A270352 A270353 * A270355 A270356 A270357

KEYWORD

nonn,frac,easy

AUTHOR

Clark Kimberling, Mar 17 2016

STATUS

approved

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Last modified August 12 04:52 EDT 2022. Contains 356067 sequences. (Running on oeis4.)