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Numerators of convergents to cube root of 5.
(Formerly M1429 N0563)
3

%I M1429 N0563 #23 Jul 04 2024 20:06:46

%S 1,2,5,12,53,171,566,737,4251,4988,9239,41944,428679,7329487,7758166,

%T 115943811,123701977,239645788,731522646953,731762292741,

%U 1463284939694,2195047232435,3658332172129,5853379404564,9511711576693,24876802557950,59265316692593

%N Numerators of convergents to cube root of 5.

%D D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 67.

%D P. Seeling, Verwandlung der irrationalen Groesse ... in einen Kettenbruch, Archiv. Math. Phys., 46 (1866), 80-120.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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

%H Vincenzo Librandi, <a href="/A002358/b002358.txt">Table of n, a(n) for n = 0..999</a>

%t Numerator[Convergents[5^(1/3), 30]] (* _Vincenzo Librandi_, Sep 08 2013 *)

%o (PARI) a(n)= contfracpnqn(contfrac(5^(1/3), n))[1, 1]; \\ _Michel Marcus_, Sep 07 2013

%Y Cf. A002357 (denominators), A005481.

%K nonn,frac

%O 0,2

%A _N. J. A. Sloane_, _Herman P. Robinson_

%E More terms from _Vincenzo Librandi_, Sep 08 2013