A089267 Continued fraction expansion with iterated 3-fold symmetry.

0, 1, 1, 23, 1, 2, 1, 18815, 3, 1, 23, 3, 1, 23, 1, 2, 1, 106597754640383, 3, 1, 23, 1, 3, 23, 1, 3, 18815, 1, 2, 1, 23, 3, 1, 23, 1, 2, 1, 18815, 3, 1, 23, 3, 1, 23, 1, 2, 1, 1715738475058821295603924428015888899408203312889855, 3, 1

Offset: 1

Author

Ralf Stephan, Oct 30 2003

Keywords

• nonn
• cofr
• nice

Links

• H. Cohn, Symmetry and specializability in continued fractions

Crossrefs

Cf. A007400.

Programs

Mathematica

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 *)

PARI

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

PARI

contfrac(suminf(k=0,1/polchebyshev(4^k,1,2))) \\ Charles R Greathouse IV, May 28 2015

Formula

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