A002211 Continued fraction for Khintchine's constant. (Formerly M0118 N0047)

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

0,1

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

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

Example

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

Mathematica

ContinuedFraction[Khinchin, 100]

Crossrefs

Cf. A002210.

Sequence in context: A371136 A245841 A011404 * A308947 A175011 A211700

Adjacent sequences: A002208 A002209 A002210 * A002212 A002213 A002214

Keyword

cofr,nonn,nice,easy

Author

N. J. A. Sloane

Extensions

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

Status

approved