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A041150 Numerators of continued fraction convergents to sqrt(85). 10
9, 37, 46, 83, 378, 6887, 27926, 34813, 62739, 285769, 5206581, 21112093, 26318674, 47430767, 216041742, 3936182123, 15960770234, 19896952357, 35857722591, 163327842721, 2975758891569, 12066363408997 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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).

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

MATHEMATICA

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

CROSSREFS

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

A041550.

Sequence in context: A274769 A126914 A273594 * A042021 A137184 A153244

Adjacent sequences:  A041147 A041148 A041149 * A041151 A041152 A041153

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified March 20 15:43 EDT 2019. Contains 321345 sequences. (Running on oeis4.)