A040074 -id:A040074 - cp's OEIS frontend

A010535 Decimal expansion of square root of 84.

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

Offset: 1

N. J. A. Sloane

Continued fraction expansion is 9 followed by {6, 18} repeated. - Harry J. Smith, Jun 10 2009

			9.165151389911680013176094387456016977968913153535943805214484247813736...

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

Cf. A040074 Continued fraction.

RealDigits[N[84^(1/2),200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Jan 23 2012 *)

{ default(realprecision, 20080); x=sqrt(84); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010535.txt", n, " ", d)); } \\ Harry J. Smith, Jun 10 2009

A041149 Denominators of continued fraction convergents to sqrt(84).

Original entry on oeis.org

1, 6, 109, 660, 11989, 72594, 1318681, 7984680, 145042921, 878242206, 15953402629, 96598657980, 1754729246269, 10624974135594, 193004263686961, 1168650556257360, 21228714276319441, 128540936214174006, 2334965566131451549, 14138334333002883300

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 (0,110,0,-1).

Cf. A041148, A040074, A020841, A010535.

I:=[1, 6, 109, 660]; [n le 4 select I[n] else 110*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 11 2013

Denominator/@Convergents[Sqrt[84], 50] (* Vladimir Joseph Stephan Orlovsky, Jul 05 2011 *)
CoefficientList[Series[(1 + 6 x - x^2)/(x^4 - 110 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 11 2013 *)

G.f.: -(x^2-6*x-1) / (x^4-110*x^2+1). - Colin Barker, Nov 13 2013

a(n) = 110*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 11 2013

cp's OEIS Frontend

A010535 Decimal expansion of square root of 84.

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