A100611 - OEIS

A100611

Continued fraction expansion of (Khinchin + (4+Khinchin*Khinchin)^(1/2))/2 [A100485], where Khinchin is Khinchin's constant (A002210).

3, 59, 8, 1, 2, 1, 1, 1, 1, 1, 2, 6, 1, 1, 3, 2, 1, 7, 1, 3, 2, 8, 5, 1, 3, 2, 6, 1, 2, 2, 2, 7, 1, 1, 3, 1, 10, 3, 1, 1, 3, 1, 1, 1, 2, 2, 3, 1, 1, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 5, 9, 2, 1, 21, 3, 1, 1, 2, 1, 13, 1, 3, 1, 1, 1, 1, 2, 2, 1, 3, 5, 1, 1, 2, 1, 3, 1, 1, 6, 4, 2, 1, 2, 1, 2, 9, 5, 16, 4, 1, 2, 2, 4

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OFFSET

0,1

COMMENTS

The geometric mean of the first 5000 partial quotients (Product[a(n),{n,1,5000}]^(1/5000)), approximately 2.6289, suggests this constant's partial quotients do indeed converge to Khinchin's constant.

LINKS

Table of n, a(n) for n=0..102.

MATHEMATICA

ContinuedFraction[(Khinchin + (4+Khinchin*Khinchin)^(1/2))/2, 130]

CROSSREFS

Cf. A100485 (decimal expansion), A002210.

Sequence in context: A049661 A295409 A184950 * A359069 A139882 A139874

Adjacent sequences: A100608 A100609 A100610 * A100612 A100613 A100614

KEYWORD

base,cofr,nonn

AUTHOR

Joseph Biberstine (jrbibers(AT)indiana.edu), Dec 01 2004

EXTENSIONS

Offset changed by Andrew Howroyd, Aug 04 2024

STATUS

approved