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Numerators of convergents to cube root of 4.
(Formerly M0881 N0335)
3

%I M0881 N0335 #27 Jul 04 2024 20:01:29

%S 1,2,3,8,19,27,100,227,781,1008,3805,4813,148195,153008,760227,913235,

%T 2586697,24193508,147747745,615184488,762932233,1378116721,3519165675,

%U 26012276446,55543718567,192643432147,440830582861,633474015008,4241674672909,4875148687917

%N Numerators of convergents to cube root of 4.

%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="/A002356/b002356.txt">Table of n, a(n) for n = 0..999</a>

%t Numerator[Convergents[Power[4, (3)^-1], 30]] (* _Vincenzo Librandi_, Aug 24 2013 *)

%o (PARI) a(n) = contfracpnqn(contfrac(4^(1/3), n))[1][1]; \\ _Michel Marcus_, Aug 23 2013

%Y Cf. A002355 (denominators), A005480.

%K nonn,frac

%O 0,2

%A _N. J. A. Sloane_

%E More terms from _Herman P. Robinson_

%E More terms from _Vincenzo Librandi_, Aug 24 2013

%E Offset changed by _Andrew Howroyd_, Jul 04 2024