login
A270477
Denominators of r-Egyptian fraction expansion for sqrt(1/3), where r(k) = 1/Prime(k).
1
1, 5, 19, 909, 709338, 4794024440479, 18787437394610419733587349, 438597049892989902759955952867127541411726874886473, 175915259950103387380668466916070098283235189077796884344520632101017268238077131833609385455236441012
OFFSET
1,2
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
sqrt(1/3) = 1/(2*1) + 1/(3*5) + 1/(5*19) + 1/(7*909) + ...
MATHEMATICA
r[k_] := 1/Prime[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[1/3]; Table[n[x, k], {k, 1, z}]
CROSSREFS
Sequence in context: A072526 A095218 A119964 * A279256 A174490 A280034
KEYWORD
nonn,frac,easy
AUTHOR
Clark Kimberling, Mar 30 2016
STATUS
approved