A100485 -id:A100485 - cp's OEIS frontend

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

Offset: 0

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

base
cofr
nonn

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.

Cf. A100485 (decimal expansion), A002210.

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

Offset changed by Andrew Howroyd, Aug 04 2024

cp's OEIS Frontend

A100611 Continued fraction expansion of (Khinchin + (4+Khinchin*Khinchin)^(1/2))/2 [A100485], where Khinchin is Khinchin's constant (A002210).

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