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

1,4

Links

Table of n, a(n) for n=1..50.

H. Cohn, Symmetry and specializability in continued fractions

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A007400.

Sequence in context: A015151 A040539 A040540 * A040538 A040537 A040542

Adjacent sequences: A089264 A089265 A089266 * A089268 A089269 A089270

Keyword

nonn,cofr,nice

Author

Ralf Stephan, Oct 30 2003

Status

approved