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A089267 Continued fraction expansion with iterated 3-fold symmetry. 2
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 (list; graph; refs; listen; history; text; internal format)
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, inf, 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-Fran├žois 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

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Last modified April 5 23:11 EDT 2020. Contains 333260 sequences. (Running on oeis4.)