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A069139 Egyptian fraction for square root of 1/2. 25

%I

%S 2,5,141,68575,32089377154,1644444237306316731482,

%T 65593236350142721999718859354569312622907814,

%U 55836140966941396682452590821074724094286247680248793718758259857815239633935672711970868

%N Egyptian fraction for square root of 1/2.

%H <a href="/index/Ed#Egypt">Index entries for sequences related to Egyptian fractions</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EgyptianFraction.html">Egyptian Fraction</a>

%F a(n) =ceiling[1/sqrt(2)-Sum_i{i<n}1/a(i)]

%e 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).

%t a = {}; k = N[1/Sqrt[2], 1000]; Do[s = Ceiling[1/k]; AppendTo[a, s]; k = k - 1/s, {n, 1, 10}]; a [From _Artur Jasinski_, Sep 22 2008]

%Y Cf. A006487.

%K nonn

%O 0,1

%A _Henry Bottomley_, Apr 08 2002

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Last modified February 22 17:14 EST 2020. Contains 332140 sequences. (Running on oeis4.)