A040099 -id:A040099 - cp's OEIS frontend

A176221 Decimal expansion of sqrt(110).

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

Offset: 2

Klaus Brockhaus, Apr 12 2010

Continued fraction expansion of sqrt(110) is A040099.

			sqrt(110) = 10.48808848170151546991...

Daniel Starodubtsev, Table of n, a(n) for n = 2..10000
Index entries for algebraic numbers, degree 2.

Cf. A010467 (decimal expansion of sqrt(10)), A010468 (decimal expansion of sqrt(11)), A040099.

RealDigits[Sqrt[110], 10, 110][[1]] (* Alonso del Arte, Jan 06 2013 *)

PARI
```
sqrt(110) \\ Amiram Eldar, Aug 04 2022
```

Equals 10 * Sum_{k>=0} binomial(2*k,k)/44^k. - Amiram Eldar, Aug 04 2022

A041199 Denominators of continued fraction convergents to sqrt(110).

Original entry on oeis.org

1, 2, 41, 84, 1721, 3526, 72241, 148008, 3032401, 6212810, 127288601, 260790012, 5343088841, 10946967694, 224282442721, 459511853136, 9414519505441, 19288550864018, 395185536785801, 809659624435620, 16588378025498201, 33986415675432022

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 (0,42,0,-1).

Cf. A041198, A176221, A040099.

Denominator[Convergents[Sqrt[110],30]] (* Harvey P. Dale, Oct 10 2012 *)
CoefficientList[Series[(1 + 2 x - x^2)/(1 - 42 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 12 2013*)

G.f.: -(x^2-2*x-1) / (x^4-42*x^2+1). - Colin Barker, Nov 14 2013

More terms from Colin Barker, Nov 14 2013

cp's OEIS Frontend

A176221 Decimal expansion of sqrt(110).

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