A041150 Numerators of continued fraction convergents to sqrt(85).

9, 37, 46, 83, 378, 6887, 27926, 34813, 62739, 285769, 5206581, 21112093, 26318674, 47430767, 216041742, 3936182123, 15960770234, 19896952357, 35857722591, 163327842721, 2975758891569, 12066363408997

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• frac
• easy

Comments

From Johannes W. Meijer, Jun 17 2010: (Start)

The a(n) terms of this sequence can be constructed with the terms of sequence A087798.

For the terms of the periodic sequence of the continued fraction for sqrt(85) see A010158. We observe that its period is five. The decimal expansion of sqrt(85) is A010536. (End)

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,756,0,0,0,0,1).

Crossrefs

Cf. A010536, A041018, A041046, A041090, A041150, A041151, A041226, A041318, A041426,

A041550.

Programs

Mathematica

Numerator[Convergents[Sqrt[85], 30]] (* Vincenzo Librandi, Oct 29 2013 *)

Formula

From Johannes W. Meijer, Jun 17 2010: (Start)

a(5*n) = A087798(3*n+1), a(5*n+1) = (A087798(3*n+2) - A087798(3*n+1))/2, a(5*n+2) = (A087798(3*n+2) + A087798(3*n+1))/2, a(5*n+3) = A087798(3*n+2) and a(5*n+4) = A087798(3*n+3)/2. (End)

G.f.: -(x^9-9*x^8+37*x^7-46*x^6+83*x^5+378*x^4+83*x^3+46*x^2+37*x+9) / (x^10+756*x^5-1). - Colin Barker, Nov 04 2013