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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
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.
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: A087358 A379644 A255357 * A057736 A181263 A130309
KEYWORD
nonn,frac,easy
AUTHOR
Clark Kimberling, Mar 15 2016
STATUS
approved