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A269996 Denominators of r-Egyptian fraction expansion for sqrt(3) - 1, where r = (1,1/2,1/3,1/4,...) 2
2, 3, 6, 26, 939, 800567, 626897816036, 732632470241183632257841, 31706715561023122142248280773186018287458544854469, 1666726692230759969765850044548001173784581299264219742879080654883940143766478552206863259848365362 (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..13

Eric Weisstein's World of Mathematics, Egyptian Fraction

Index entries for sequences related to Egyptian fractions

EXAMPLE

sqrt(3) - 1 = 1/2 + 1/(2*3) + 1/(3*6) + ...

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 = Sqrt[3] - 1; Table[n[x, k], {k, 1, z}]

CROSSREFS

Cf. A269993.

Sequence in context: A144857 A090445 A228346 * A018318 A277809 A051717

Adjacent sequences:  A269993 A269994 A269995 * A269997 A269998 A269999

KEYWORD

nonn,frac,easy

AUTHOR

Clark Kimberling, Mar 15 2016

STATUS

approved

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Last modified January 21 05:39 EST 2020. Contains 331104 sequences. (Running on oeis4.)