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A270314 Denominators of r-Egyptian fraction expansion for log(2), where r = (1,1/2,1/3,1/4,...). 2
2, 3, 13, 298, 355823, 306479173303, 85372761970827958806466, 16575976283809775714654644103484953548013865676, 269025959411335919672976939610798847100114463059537709191005089031919232139117472577538965440 (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
Eric Weisstein's World of Mathematics, Egyptian Fraction
EXAMPLE
log(2) = 1/2 + 1/(2*3) + 1/(3*13) + ...
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 = Log[2]; Table[n[x, k], {k, 1, z}]
CROSSREFS
Cf. A269993.
Sequence in context: A119564 A132358 A090100 * A132484 A258357 A160858
KEYWORD
nonn,frac,easy
AUTHOR
Clark Kimberling, Mar 15 2016
STATUS
approved

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Last modified July 21 14:09 EDT 2024. Contains 374474 sequences. (Running on oeis4.)