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A270476
Denominators of r-Egyptian fraction expansion for sqrt(1/2), where r(k) = 1/Prime(k).
2
1, 2, 5, 325, 164073, 23835564403, 509747166181000498873, 590605960011761211516665913403247265840072, 493340534610970903685535778248091335992630045997033895220604001625216391426083646793
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(1/2) = 1/(2*1) + 1/(3*2) + 1/(5*5) + 1/(7*325) + ...
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[1/2]; Table[n[x, k], {k, 1, z}]
CROSSREFS
Sequence in context: A353050 A308270 A042909 * A345977 A183129 A081462
KEYWORD
nonn,frac,easy
AUTHOR
Clark Kimberling, Mar 30 2016
STATUS
approved