login
Numerators of continued fraction convergents to cube root of 7.
(Formerly M2127)
3

%I M2127 #25 Jul 05 2024 10:07:14

%S 1,2,21,44,725,1494,2219,10370,22959,33329,722868,756197,2991459,

%T 15713492,18704951,53123394,71828345,124951739,321731823,3664001792,

%U 18641740783,22305742575,85558968508,107864711083,301288390674,8242651259281,33271893427798,41514544687079

%N Numerators 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="/A005484/b005484.txt">Table of n, a(n) for n = 0..999</a>

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

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

%Y Cf. A005482, A005483, A005485 (denominators).

%K nonn,frac

%O 0,2

%A _N. J. A. Sloane_, _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