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Denominators of convergents to cube root of 4.
(Formerly M1407 N0549)
3

%I M1407 N0549 #28 Jul 04 2024 20:01:15

%S 1,1,2,5,12,17,63,143,492,635,2397,3032,93357,96389,478913,575302,

%T 1629517,15240955,93075247,387541943,480617190,868159133,2216935456,

%U 16386707325,34990350106,121357757643,277705865392,399063623035,2672087603602,3071151226637

%N Denominators 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="/A002355/b002355.txt">Table of n, a(n) for n = 0..999</a>

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

%o (PARI) a(n) = contfracpnqn(contfrac(4^(1/3), n))[2, 1]; \\ _Michel Marcus_, Aug 23 2013

%Y Cf. A002356 (numerators), A005480.

%K nonn,frac

%O 0,3

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

%E More terms from _Vincenzo Librandi_, Aug 24 2013

%E Offset changed by _Andrew Howroyd_, Jul 04 2024