login
Continued fraction expansion with iterated 3-fold symmetry.
2

%I #11 Apr 23 2021 11:48:37

%S 0,1,1,23,1,2,1,18815,3,1,23,3,1,23,1,2,1,106597754640383,3,1,23,1,3,

%T 23,1,3,18815,1,2,1,23,3,1,23,1,2,1,18815,3,1,23,3,1,23,1,2,1,

%U 1715738475058821295603924428015888899408203312889855,3,1

%N Continued fraction expansion with iterated 3-fold symmetry.

%H H. Cohn, <a href="http://arXiv.org/abs/math.NT/0008221">Symmetry and specializability in continued fractions</a>

%F Sum_{k=0..infinity} 1/chebyshev(4^k, 2) = 0.51030927976262776140...

%t nmax = 50; f[m_] := ContinuedFraction[ Sum[ 1/ChebyshevT[4^k, 2], {k, 0, m}]]; A089267 = Catch[ For[m = 1, True, m++, If[ Length[fm = f[m]] > nmax, Throw[ fm[[1 ;; nmax]] ]]]] (* _Jean-François Alcover_, Sep 19 2012 *)

%o (PARI) contfrac(suminf(k=0,1/subst(poltchebi(4^k),x,2)))

%o (PARI) contfrac(suminf(k=0,1/polchebyshev(4^k,1,2))) \\ _Charles R Greathouse IV_, May 28 2015

%Y Cf. A007400.

%K nonn,cofr,nice

%O 1,4

%A _Ralf Stephan_, Oct 30 2003