A144835 Denominators of an Egyptian fraction for 1/zeta(2) = 0.607927101854... (A059956).
2, 10, 127, 18838, 522338493, 727608914652776081, 990935377560451600699026552443764271, 1223212384013602554473872691328685513734082755736750146553750539914774364
Offset: 1
Examples
1/zeta(2) = 0.607927101854... = 1/2 + 1/10 + 1/127 + 1/18838 + ...
Links
- Amiram Eldar, Table of n, a(n) for n = 1..11
- Mohammad K. Azarian, Sylvester's Sequence and the Infinite Egyptian Fraction Decomposition of 1, Problem 958, College Mathematics Journal, Vol. 42, No. 4, September 2011, p. 330. Solution published in Vol. 43, No. 4, September 2012, pp. 340-342.
- Eric Weisstein's World of Mathematics, Egyptian Fraction.
- Index entries for sequences related to Egyptian fractions.
Crossrefs
Programs
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Mathematica
a = {}; k = N[1/Zeta[2], 1000]; Do[s = Ceiling[1/k]; AppendTo[a, s]; k = k - 1/s, {n, 1, 10}]; a -
PARI
x=1/zeta(2); while(x, t=1\x+1; print1(t", "); x -= 1/t) \\ Charles R Greathouse IV, Nov 08 2013