A010157 -id:A010157 - cp's OEIS frontend

A010531 Decimal expansion of square root of 79.

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

Offset: 1

N. J. A. Sloane

Continued fraction expansion is 8 followed by {1, 7, 1, 16} repeated. - Harry J. Smith, Jun 09 2009

			8.888194417315588850091441675408727817076450603729526298354720116376100...

Harry J. Smith, Table of n, a(n) for n = 1..20000
Index entries for algebraic numbers, degree 2.

Cf. A010157 Continued fraction.

RealDigits[N[Sqrt[79],200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Feb 04 2012 *)

{ default(realprecision, 20080); x=sqrt(79); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010531.txt", n, " ", d)); } \\ Harry J. Smith, Jun 09 2009

A041141 Denominators of continued fraction convergents to sqrt(79).

Original entry on oeis.org

1, 1, 8, 9, 152, 161, 1279, 1440, 24319, 25759, 204632, 230391, 3890888, 4121279, 32739841, 36861120, 622517761, 659378881, 5238169928, 5897548809, 99598950872, 105496499681, 838074448639, 943570948320, 15935209621759, 16878780570079

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 (0,0,0,160,0,0,0,-1).

Cf. A041140, A010157, A020836, A010531.

I:=[1,1,8,9,152,161,1279,1440]; [n le 8 select I[n] else 160*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 11 2013

Denominator/@Convergents[Sqrt[79], 50] (* Vladimir Joseph Stephan Orlovsky, Jul 05 2011 *)
CoefficientList[Series[-(x^2 - x - 1) (x^4 + 9 x^2 + 1)/(x^8 - 160 x^4 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 11 2013 *)
LinearRecurrence[{0,0,0,160,0,0,0,-1},{1,1,8,9,152,161,1279,1440},40] (* Harvey P. Dale, Aug 09 2021 *)

G.f.: -(x^2-x-1)*(x^4+9*x^2+1) / (x^8-160*x^4+1). - Colin Barker, Nov 13 2013

a(n) = 160*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 11 2013

cp's OEIS Frontend

A010531 Decimal expansion of square root of 79.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI