A010213 -id:A010213 - cp's OEIS frontend

A178592 Decimal expansion of sqrt(165).

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

Offset: 2

Klaus Brockhaus, May 30 2010

Continued fraction expansion of sqrt(165) is A010213.

			sqrt(165) = 12.84523257866512902011...

G. C. Greubel, Table of n, a(n) for n = 2..10001

Cf. A178591 (decimal expansion of (9+sqrt(165))/14), A010213 (12 followed by (repeat 1, 5, 2, 5, 1, 24)).

SetDefaultRealField(RealField(100)); Sqrt(165); // G. C. Greubel, Jan 30 2019

RealDigits[Sqrt[165],10,120][[1]] (* Harvey P. Dale, May 30 2012 *)

default(realprecision, 100); sqrt(165) \\ G. C. Greubel, Jan 30 2019

numerical_approx(sqrt(165), digits=100) # G. C. Greubel, Jan 30 2019

A041305 Denominators of continued fraction convergents to sqrt(165).

Original entry on oeis.org

1, 1, 6, 13, 71, 84, 2087, 2171, 12942, 28055, 153217, 181272, 4503745, 4685017, 27928830, 60542677, 330642215, 391184892, 9719079623, 10110264515, 60270402198, 130651068911, 713525746753, 844176815664, 20973769322689, 21817946138353

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 (0,0,0,0,0,2158,0,0,0,0,0,-1).

Cf. A041304, A010213, A178592.

I:=[1,1,6,13,71,84,2087,2171,12942,28055,153217, 181272]; [n le 12 select I[n] else 2158*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 15 2013

Denominator[Convergents[Sqrt[165], 30]] (* Vincenzo Librandi, Dec 15 2013 *)

G.f.: -(x^10 -x^9 +6*x^8 -13*x^7 +71*x^6 -84*x^5 -71*x^4 -13*x^3 -6*x^2 -x -1) / ((x^4 -13*x^2 +1)*(x^8 +13*x^6 +168*x^4 +13*x^2 +1)). - Colin Barker, Nov 15 2013

a(n) = 2158*a(n-6) - a(n-12). - Vincenzo Librandi, Dec 15 2013

More terms from Colin Barker, Nov 15 2013

cp's OEIS Frontend

A178592 Decimal expansion of sqrt(165).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Sage