A002355 -id:A002355 - cp's OEIS frontend

A002356 Numerators of convergents to cube root of 4.

1, 2, 3, 8, 19, 27, 100, 227, 781, 1008, 3805, 4813, 148195, 153008, 760227, 913235, 2586697, 24193508, 147747745, 615184488, 762932233, 1378116721, 3519165675, 26012276446, 55543718567, 192643432147, 440830582861, 633474015008, 4241674672909, 4875148687917

Offset: 0

N. J. A. Sloane

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. A002355 (denominators), A005480.

Numerator[Convergents[Power[4, (3)^-1], 30]] (* Vincenzo Librandi, Aug 24 2013 *)

a(n) = contfracpnqn(contfrac(4^(1/3), n))[1][1]; \\ Michel Marcus, Aug 23 2013

More terms from Herman P. Robinson
More terms from Vincenzo Librandi, Aug 24 2013
Offset changed by Andrew Howroyd, Jul 04 2024

A002947 Continued fraction for cube root of 4.

Original entry on oeis.org

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

N. J. A. Sloane

			4^(1/3) = 1.58740105196819947... = 1 + 1/(1 + 1/(1 + 1/(2 + 1/(2 + ...)))). - _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.
Gang Xiao, Contfrac
Index entries for continued fractions for constants

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

Cf. A002355, A002356 (convergents).

[ContinuedFraction(4^(1/3))]; // Vincenzo Librandi, Aug 02 2015

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

{ 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

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

Offset changed by Andrew Howroyd, Jul 04 2024

cp's OEIS Frontend

A002356 Numerators of convergents to cube root of 4.

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