A002211 Continued fraction for Khintchine's constant.

2, 1, 2, 5, 1, 1, 2, 1, 1, 3, 10, 2, 1, 3, 2, 24, 1, 3, 2, 3, 1, 1, 1, 90, 2, 1, 12, 1, 1, 1, 1, 5, 2, 6, 1, 6, 3, 1, 1, 2, 5, 2, 1, 2, 1, 1, 4, 1, 2, 2, 3, 2, 1, 1, 4, 1, 1, 2, 5, 2, 1, 1, 3, 29, 8, 3, 1, 4, 3, 1, 10, 50, 1, 2, 2, 7, 6, 2, 2, 16, 4, 4, 2, 2, 3, 1, 1, 7, 1, 5, 1, 2, 1, 5, 3, 1

Offset: 0

Author

N. J. A. Sloane

Keywords

• cofr
• nonn
• nice
• easy

Comments

Incrementally larger terms in the continued fraction for Khintchine's constant: 1, 2, 5, 10, 24, 90, 770, 941, 11759, 54097, 231973, ..., and they occur at 1, 2, 3, 10, 15, 23, 104, 1701, 2445, 18995, 60037, ... - Robert G. Wilson v, Dec 09 2013

Examples

			2.685452001065306445309714835... = 2 + 1/(1 + 1/(2 + 1/(5 + 1/(1 + ...))))
[a_0; a_1, a_2, ...] = [2, 1, 2, ...]
		

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• T. D. Noe, Table of n, a(n) for n = 0..999
• H. Havermann, Simple Continued Fraction Expansion of Khinchin's Constant
• D. Shanks and J. W. Wrench, Jr., Khintchine's constant, Amer. Math. Monthly, 66 (1959), 276-279.
• J. W. Wrench, Further evaluation of Khintchine's constant, Math. Comp., 14 (1960), 370-371.
• J. W. Wrench, Jr. and D. Shanks, Questions concerning Khintchine's constant and the efficient computation of regular continued fractions, Math. Comp., 20 (1966), 444-448.
• G. Xiao, Contfrac
• Eric Weisstein's World of Mathematics, Khinchin's Constant Continued Fraction
• Index entries for continued fractions for constants

Crossrefs

Cf. A002210.

Programs

Mathematica

ContinuedFraction[Khinchin, 100]

Extensions

More terms from Robert G. Wilson v, Oct 31 2001