A040195 -id:A040195 - cp's OEIS frontend

A176441 Decimal expansion of sqrt(210).

1, 4, 4, 9, 1, 3, 7, 6, 7, 4, 6, 1, 8, 9, 4, 3, 8, 5, 7, 3, 7, 1, 8, 6, 6, 4, 1, 5, 7, 1, 6, 9, 7, 7, 1, 7, 2, 3, 1, 4, 0, 1, 3, 2, 8, 7, 4, 7, 5, 8, 9, 7, 3, 0, 8, 8, 6, 9, 5, 9, 2, 4, 8, 0, 7, 1, 1, 8, 1, 4, 4, 3, 7, 2, 6, 5, 3, 6, 8, 0, 4, 2, 1, 7, 1, 2, 5, 6, 3, 1, 9, 2, 0, 0, 3, 6, 1, 7, 4, 9, 7, 7, 5, 3, 0

Offset: 2

Klaus Brockhaus, Apr 19 2010

Continued fraction expansion of sqrt(210) is A040195.

			sqrt(210) = 14.49137674618943857371...

Index entries for algebraic numbers, degree 2.

Cf. A010467 (decimal expansion of sqrt(10)), A010477 (decimal expansion of sqrt(21)), A176440 (decimal expansion of (14+sqrt(210))/4), A040195 (14 followed by (repeat 2, 28)).

RealDigits[Sqrt[210],10,120][[1]]  (* Harvey P. Dale, Apr 21 2011 *)

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

Original entry on oeis.org

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

cp's OEIS Frontend

A176441 Decimal expansion of sqrt(210).

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