A002947 Continued fraction for cube root of 4. (Formerly M0200)

1, 1, 1, 2, 2, 1, 3, 2, 3, 1, 3, 1, 30, 1, 4, 1, 2, 9, 6, 4, 1, 1, 2, 7, 2, 3, 2, 1, 6, 1, 1, 1, 25, 1, 7, 7, 1, 1, 1, 1, 266, 1, 3, 2, 1, 3, 60, 1, 5, 1, 8, 5, 6, 1, 4, 20, 1, 4, 1, 1, 14, 1, 4, 4, 1, 1, 1, 1, 7, 3, 1, 1, 2, 1, 3, 1, 4, 4, 1, 1, 1, 3, 1, 34, 8, 2, 10, 6, 3, 1, 2, 31, 1, 1, 1, 4, 3, 44, 1, 45

Offset

0,4

References

H. P. Robinson, Letter to N. J. A. Sloane, Nov 13 1973.

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

Links

Harry J. Smith, Table of n, a(n) for n = 0..19999

S. Lang and H. Trotter, Continued fractions for some algebraic numbers, J. Reine Angew. Math. 255 (1972), 112-134.

S. Lang and H. Trotter, Continued fractions for some algebraic numbers, J. Reine Angew. Math. 255 (1972), 112-134. [Annotated scanned copy]

Herman P. Robinson, Letter to N. J. A. Sloane, Nov 13 1973.

Gang Xiao, Contfrac

Index entries for continued fractions for constants

Example

4^(1/3) = 1.58740105196819947... = 1 + 1/(1 + 1/(1 + 1/(2 + 1/(2 + ...)))). - Harry J. Smith, May 08 2009

Mathematica

ContinuedFraction[4^(1/3), 80] (* Alonso del Arte, Jul 24 2015 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(4^(1/3)); for (n=1, 20000, write("b002947.txt", n-1, " ", x[n])); } \\ Harry J. Smith, May 08 2009
(Magma) [ContinuedFraction(4^(1/3))]; // Vincenzo Librandi, Aug 02 2015

Crossrefs

Cf. A005480 (decimal expansion). - Harry J. Smith, May 08 2009

Cf. A002355, A002356 (convergents).

Sequence in context: A130816 A109951 A116608 * A241605 A128180 A209279

Adjacent sequences: A002944 A002945 A002946 * A002948 A002949 A002950

Keyword

nonn,cofr,easy

Author

N. J. A. Sloane

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 29 2003

Offset changed by Andrew Howroyd, Jul 04 2024

Status

approved