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Continued fraction for sixth root of 6.
1

%I #28 Aug 09 2024 01:54:18

%S 1,2,1,6,1,9,1,1,1,2,4,9,4,4,2,2,1,8,1,2,21,10,1,13,4,1,6,2,10,2,2,3,

%T 1,12,3,2,1,1,2,1,9,7,3,1,4,2,8,1,11,1,2,4,3,1,7,6,1,1,1,11,1,2,1,9,1,

%U 2,1,2,9,44,1,1,1,1,34,1,12,1,3,2,3,54,1

%N Continued fraction for sixth root of 6.

%H Robert Israel, <a href="/A274085/b274085.txt">Table of n, a(n) for n = 0..1999</a>

%H <a href="/index/Con#confC">Index entries for continued fractions for constants</a>

%e 6^(1/6) = 1 + 1/(2 + 1/(1 + 1/(6 + 1/(1 + ...)))).

%p numtheory:-cfracpol(x^6-6,100)[2]; # _Robert Israel_, Jul 31 2016

%t ContinuedFraction[6^(1/6), {80}] (* _Alonso del Arte_, Jun 18 2016 *)

%o (PARI) default(realprecision, 210); contfrac(6^(1/6))

%Y Cf. A011215 (decimal expansion).

%K nonn,cofr

%O 0,2

%A _Douglas de Araujo Smigly_, Jun 09 2016