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%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
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