A069139 Egyptian fraction for square root of 1/2.

2, 5, 141, 68575, 32089377154, 1644444237306316731482, 65593236350142721999718859354569312622907814

Offset: 0

Author

Henry Bottomley, Apr 08 2002

Keywords

• nonn

Examples

			a(3) = 68575 since sqrt(1/2) = 0.707106781186..., 1/2 + 1/5 + 1/141 + 1/68574 = 0.707106781368... (which is too much) and 1/2 + 1/5 + 1/141 + 1/68575 = 0.707106781155... (which is not too much).
		

Links

• Jinyuan Wang, Table of n, a(n) for n = 0..10
• Eric Weisstein's World of Mathematics, Egyptian Fraction.
• Index entries for sequences related to Egyptian fractions

Crossrefs

Cf. A006487, A010503 (sqrt(1/2)).

Programs

Mathematica

a = {}; k = N[1/Sqrt[2], 1000]; Do[s = Ceiling[1/k]; AppendTo[a, s]; k = k - 1/s, {n, 1, 10}]; a (* Artur Jasinski, Sep 22 2008 *)

Formula

a(n) = ceiling(1/(1/sqrt(2) - Sum_{i=0..n-1} 1/a(i))).