A002354 - OEIS

%I M2830 N1140 #29 Jul 04 2024 20:40:59

%S 1,3,10,13,62,75,437,512,949,6206,13361,73011,597449,1865358,6193523,

%T 26639450,59472423,383473988,1593368375,6756947488,8350315863,

%U 31807895077,71966106017,247706213128,1062790958529,1310497171657,6304779645157,58053513978070

%N Numerators of convergents to cube root of 3.

%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="/A002354/b002354.txt">Table of n, a(n) for n = 0..999</a>

%t Numerator[Convergents[3^(1/3), 30]] (* _Vincenzo Librandi_, Sep 09 2013 *)

%o (PARI) a(n)= contfracpnqn(contfrac(3^(1/3), n))[1, 1];  \\ _Michel Marcus_, Sep 08 2013

%Y Cf. A002353 (denominators), A002581.

%K nonn,frac

%O 0,2

%A _N. J. A. Sloane_

%E More terms from _Herman P. Robinson_

%E More terms from _Michel Marcus_, Sep 08 2013

%E Offset changed by _Andrew Howroyd_, Jul 04 2024