A041390 -id:A041390 - cp's OEIS frontend

A041391 Denominators of continued fraction convergents to sqrt(210).

1, 2, 57, 116, 3305, 6726, 191633, 389992, 11111409, 22612810, 644270089, 1311152988, 37356553753, 76024260494, 2166035847585, 4408095955664, 125592722606177, 255593541168018, 7282211875310681, 14820017291789380, 422242696045413321

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (0,58,0,-1).

Cf. A041390, A176441, A040195.

I:=[1,2,57,116]; [n le 4 select I[n] else 58*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 17 2013

Denominator[Convergents[Sqrt[210], 30]] (* Vincenzo Librandi, Dec 17 2013 *)

G.f.: -(x^2-2*x-1) / (x^4-58*x^2+1). - Colin Barker, Nov 17 2013

a(n) = 58*a(n-2) - a(n-4) for n>3. - Vincenzo Librandi, Dec 17 2013

More terms from Colin Barker, Nov 17 2013

A040195 Continued fraction for sqrt(210).

Original entry on oeis.org

14, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28

Offset: 0

N. J. A. Sloane

Cf. A176441 (decimal expansion), A041390, A041391 (convergents).

with(numtheory): Digits := 300: convert(evalf(sqrt(210)),confrac);

ContinuedFraction[Sqrt[210], 100] (* or *)
PadRight[{14}, 100, {28, 2}] (* Paolo Xausa, Sep 17 2024 *)

cp's OEIS Frontend

A041391 Denominators of continued fraction convergents to sqrt(210).

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