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Numerators of continued fraction convergents to fifth root of 2.
(Formerly M4336 N1815)
3

%I M4336 N1815 #32 Jul 05 2024 11:04:13

%S 1,7,8,23,31,54,85,309,7810,8119,40286,128977,427217,3119496,

%T 162641009,165760505,494162019,1648246562,3790655143,58508073707,

%U 120806802557,300121678821,1321293517841,21440817964277,44202929446395,330861324089042,375064253535437

%N Numerators of continued fraction convergents to fifth root of 2.

%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="/A002362/b002362.txt">Table of n, a(n) for n = 0..999</a>

%t Numerator[Convergents[2^(1/5), 30]] (* _Vincenzo Librandi_, Sep 08 2013 *)

%o (PARI) a(n)= contfracpnqn(contfrac(2^(1/5), n+1))[1, 1]; \\ _Michel Marcus_, Sep 07 2013

%Y Cf. A002361 (denominators), A002950, A005531.

%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 07 2013

%E a(26)-a(27) corrected by _Vincenzo Librandi_, Sep 08 2013

%E Offset changed by _Andrew Howroyd_, Jul 05 2024