A010152 -id:A010152 - cp's OEIS frontend

A010526 Decimal expansion of square root of 74.

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

Offset: 1

N. J. A. Sloane

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

			8.602325267042626771729473535049713632027535557290735619508045641237426...

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

Cf. A010152 Continued fraction.

RealDigits[N[74^(1/2),200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Jan 23 2012 *)

{ default(realprecision, 20080); x=sqrt(74); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010526.txt", n, " ", d)); } \\ Harry J. Smith, Jun 09 2009

A041131 Denominators of continued fraction convergents to sqrt(74).

Original entry on oeis.org

1, 1, 2, 3, 5, 83, 88, 171, 259, 430, 7139, 7569, 14708, 22277, 36985, 614037, 651022, 1265059, 1916081, 3181140, 52814321, 55995461, 108809782, 164805243, 273615025, 4542645643, 4816260668, 9358906311, 14175166979, 23534073290, 390720339619, 414254412909

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 (0,0,0,0,86,0,0,0,0,1).

Cf. A041130, A010152, A020831, A010526.

I:=[1, 1, 2, 3, 5, 83, 88, 171, 259, 430]; [n le 10 select I[n] else 86*Self(n-5)+Self(n-10): n in [1..40]]; // Vincenzo Librandi, Dec 11 2013

Denominator/@Convergents[Sqrt[74], 50] (* Vladimir Joseph Stephan Orlovsky, Jul 05 2011 *)
CoefficientList[Series[-(x^4 - 3 x^3 + 4 x^2 - 2 x + 1) (x^4 + 2 x^3 + 4 x^2 + 3 x + 1)/(x^10 + 86 x^5 - 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 11 2013 *)
LinearRecurrence[{0,0,0,0,86,0,0,0,0,1},{1,1,2,3,5,83,88,171,259,430},50] (* Harvey P. Dale, Nov 09 2017 *)

G.f.: -(x^4-3*x^3+4*x^2-2*x+1)*(x^4+2*x^3+4*x^2+3*x+1) / (x^10+86*x^5-1). - Colin Barker, Nov 13 2013

a(n) = 86*a(n-5) + a(n-10). - Vincenzo Librandi, Dec 11 2013

cp's OEIS Frontend

A010526 Decimal expansion of square root of 74.

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