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Smallest partial quotients of an infinite simple continued fraction such that the fractional remainders sum to unity.
4

%I #10 Mar 12 2015 18:31:22

%S 2,2,9,91,14201,252238179,82413709268226496,

%T 12393783734739289765092773334814410,

%U 940449499772176767594719706273493318801155215211368219531441729200804

%N Smallest partial quotients of an infinite simple continued fraction such that the fractional remainders sum to unity.

%C Conjecture: log(a(n+1))/log(a(n)) -> 2. The 9th term has 69 digits, the 10th term has 140 digits. The decimal expansion of the continued fraction: [0;2,2,9,91,14201,252238179,...] = 0.404250350307436947086987047594...

%e 1 = [0;2,2,9,91,14201,...] + [0;2,9,91,14201,...] + [0;9,91,14201,...] + [0;91,14201,...] + [0;14201,...] + ... = .40425035 + .47371461 + .11097560 + .01098900 + .00007041 + ...

%Y Cf. A081088, A081089, A081090.

%Y Cf. A081087 (decimal expansion).

%K cofr,nonn

%O 1,1

%A _Hans Havermann_ and _Paul D. Hanna_, Mar 05 2003