A040094 -id:A040094 - cp's OEIS frontend

A176461 Decimal expansion of sqrt(105).

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

Offset: 2

Klaus Brockhaus, Apr 20 2010

Continued fraction expansion of sqrt(105) is A040094.

			sqrt(105) = 10.24695076595959838322...

Cf. A002194, A002163, A010465, A176460, A040094.

RealDigits[Sqrt[105],10,120][[1]] (* Harvey P. Dale, Aug 03 2016 *)

A041189 Denominators of continued fraction convergents to sqrt(105).

Original entry on oeis.org

1, 4, 81, 328, 6641, 26892, 544481, 2204816, 44640801, 180768020, 3660001201, 14820772824, 300075457681, 1215122603548, 24602527528641, 99625232718112, 2017107181890881, 8168053960281636, 165378186387523601, 669680799510376040

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 (0,82,0,-1).

Cf. A040094, A041188 (numerators), A176461.

I:=[1,4,81,328]; [n le 4 select I[n] else 82*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 12 2013

Denominator/@Convergents[Sqrt[105],30]  (* Harvey P. Dale, Apr 02 2011 *)
CoefficientList[Series[(1 + 4 x - x^2)/(1 - 82 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 12 2013*)

G.f.: (1 + 4*x - x^2)/(1 - 82*x^2 + x^4). - Vincenzo Librandi, Dec 12 2013

a(n) = 82*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 12 2013

a(19) from Vincenzo Librandi, Dec 12 2013

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A176461 Decimal expansion of sqrt(105).

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A041189 Denominators of continued fraction convergents to sqrt(105).

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