A002357 -id:A002357 - cp's OEIS frontend

A002358 Numerators of convergents to cube root of 5.

1, 2, 5, 12, 53, 171, 566, 737, 4251, 4988, 9239, 41944, 428679, 7329487, 7758166, 115943811, 123701977, 239645788, 731522646953, 731762292741, 1463284939694, 2195047232435, 3658332172129, 5853379404564, 9511711576693, 24876802557950, 59265316692593

Offset: 0

N. J. A. Sloane, Herman P. Robinson

D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 67.
P. Seeling, Verwandlung der irrationalen Groesse ... in einen Kettenbruch, Archiv. Math. Phys., 46 (1866), 80-120.
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).

Vincenzo Librandi, Table of n, a(n) for n = 0..999

Cf. A002357 (denominators), A005481.

Numerator[Convergents[5^(1/3), 30]] (* Vincenzo Librandi, Sep 08 2013 *)

a(n)= contfracpnqn(contfrac(5^(1/3), n))[1, 1]; \\ Michel Marcus, Sep 07 2013

More terms from Vincenzo Librandi, Sep 08 2013

A002948 Continued fraction for cube root of 5.

Original entry on oeis.org

1, 1, 2, 2, 4, 3, 3, 1, 5, 1, 1, 4, 10, 17, 1, 14, 1, 1, 3052, 1, 1, 1, 1, 1, 1, 2, 2, 1, 3, 2, 1, 13, 5, 1, 1, 1, 13, 2, 41, 1, 4, 12, 1, 5, 2, 7, 1, 1, 3, 33, 2, 1, 1, 1, 1, 1, 1, 3, 2, 2, 1, 15, 12, 8, 10, 48, 1, 2, 1, 1, 3, 4, 1, 474, 1, 13, 2, 4, 1, 1, 49

Offset: 0

N. J. A. Sloane

			5^(1/3) = 1.70997594667669698... = 1 + 1/(1 + 1/(2 + 1/(2 + 1/(4 + ...)))). - _Harry J. Smith_, May 08 2009

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).

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.
G. Xiao, Contfrac
Index entries for continued fractions for constants

Cf. A005481 (decimal expansion).

Cf. A002357, A002358 (convergents).

SetDefaultRealField(RealField(100)); ContinuedFraction(5^(1/3)); // G. C. Greubel, Nov 02 2018

with(numtheory): cfrac(5^(1/3),80,'quotients'); # Muniru A Asiru, Nov 02 2018

ContinuedFraction[5^(1/3), 100] (* G. C. Greubel, Nov 02 2018 *)

{ allocatemem(932245000); default(realprecision, 21000); x=contfrac(5^(1/3)); for (n=1, 20000, write("b002948.txt", n-1, " ", x[n])); } \\ Harry J. Smith, May 08 2009

Offset changed by Andrew Howroyd, Jul 04 2024

cp's OEIS Frontend

A002358 Numerators of convergents to cube root of 5.

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