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Denominators of continued fraction convergents to cube root of 7.
(Formerly M4781)
3

%I M4781 #22 Jul 05 2024 10:07:09

%S 1,1,11,23,379,781,1160,5421,12002,17423,377885,395308,1563809,

%T 8214353,9778162,27770677,37548839,65319516,168187871,1915386097,

%U 9745118356,11660504453,44726631715,56387136168,157500904051,4308911545545,17393147086231,21702058631776

%N Denominators of continued fraction convergents to cube root of 7.

%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 and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Vincenzo Librandi, <a href="/A005485/b005485.txt">Table of n, a(n) for n = 0..999</a>

%t Denominator[Convergents[7^(1/3), 40]] (* _Vincenzo Librandi_, Sep 08 2013 *)

%o (PARI) a(n)= contfracpnqn(contfrac(7^(1/3), n))[2, 1]; \\ _Michel Marcus_, Sep 07 2013

%Y Cf. A005482, A005482, A005484 (numerators).

%K nonn,frac

%O 0,3

%A _N. J. A. Sloane_

%E More terms from _Herman P. Robinson_.

%E More terms from _Michel Marcus_, Sep 07 2013

%E Inserted a(27) by _Vincenzo Librandi_, Sep 08 2013

%E Offset changed by _Andrew Howroyd_, Jul 05 2024