A081086 - OEIS

A081086

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

2, 2, 9, 91, 14201, 252238179, 82413709268226496, 12393783734739289765092773334814410, 940449499772176767594719706273493318801155215211368219531441729200804

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OFFSET

1,1

COMMENTS

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...

LINKS

Table of n, a(n) for n=1..9.

EXAMPLE

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 + ...

CROSSREFS

Cf. A081088, A081089, A081090.

Cf. A081087 (decimal expansion).

Sequence in context: A205390 A204265 A343406 * A019514 A135816 A157341

Adjacent sequences: A081083 A081084 A081085 * A081087 A081088 A081089

KEYWORD

cofr,nonn

AUTHOR

Hans Havermann and Paul D. Hanna, Mar 05 2003

STATUS

approved

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