A010159 -id:A010159 - cp's OEIS frontend

A010537 Decimal expansion of square root of 86.

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

Offset: 1

N. J. A. Sloane

Continued fraction expansion is 9 followed by {3, 1, 1, 1, 8, 1, 1, 1, 3, 18} repeated. - Harry J. Smith, Jun 10 2009

			9.273618495495703752516416073990174626263468912076298213373826598328236...

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

Cf. A010159 (continued fraction).

RealDigits[N[Sqrt[86],200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Feb 04 2012 *)

{ default(realprecision, 20080); x=sqrt(86); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010537.txt", n, " ", d)); } \\ Harry J. Smith, Jun 10 2009

A041153 Denominators of continued fraction convergents to sqrt(86).

Original entry on oeis.org

1, 3, 4, 7, 11, 95, 106, 201, 307, 1122, 20503, 62631, 83134, 145765, 228899, 1976957, 2205856, 4182813, 6388669, 23348820, 426667429, 1303351107, 1730018536, 3033369643, 4763388179, 41140475075, 45903863254, 87044338329, 132948201583, 485888943078

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 (0,0,0,0,0,0,0,0,0,20810,0,0,0,0,0,0,0,0,0,-1).

Cf. A041152, A010159, A020843, A010537.

I:=[1, 3, 4, 7, 11, 95, 106, 201, 307, 1122, 20503, 62631, 83134, 145765, 228899, 1976957, 2205856, 4182813, 6388669, 23348820]; [n le 20 select I[n] else 20810*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 12 2013

Denominator/@Convergents[Sqrt[86], 50] (* Vladimir Joseph Stephan Orlovsky, Jul 05 2011 *)
CoefficientList[Series[-(x^18 - 3 x^17 + 4 x^16 - 7 x^15 + 11 x^14 - 95 x^13 + 106 x^12 - 201 x^11 + 307 x^10 - 1122 x^9 - 307 x^8 - 201 x^7 - 106 x^6 - 95 x^5 - 11 x^4 - 7 x^3 - 4 x^2 - 3 x - 1)/(x^20 - 20810 x^10 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 12 2013 *)

G.f.: -(x^18 -3*x^17 +4*x^16 -7*x^15 +11*x^14 -95*x^13 +106*x^12 -201*x^11 +307*x^10 -1122*x^9 -307*x^8 -201*x^7 -106*x^6 -95*x^5 -11*x^4 -7*x^3 -4*x^2 -3*x-1) / (x^20-20810*x^10+1). - Colin Barker, Nov 13 2013

a(n) = 20810*a(n-10) - a(n-20). - Vincenzo Librandi, Dec 12 2013

cp's OEIS Frontend

A010537 Decimal expansion of square root of 86.

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