A041426 Numerators of continued fraction convergents to sqrt(229).

15, 106, 121, 227, 1710, 51527, 362399, 413926, 776325, 5848201, 176222355, 1239404686, 1415627041, 2655031727, 20000849130, 602680505627, 4238764388519, 4841444894146, 9080209282665, 68402909872801, 2061167505466695, 14496575448139666, 16557742953606361

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• frac
• cofr
• easy

Comments

From Johannes W. Meijer, Jun 12 2010: (Start)

The a(n) terms of this sequence can be constructed with the terms of sequence A090301.

For the terms of the periodical sequence of the continued fraction for sqrt(229) see A040213. We observe that its period is five. (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, 3420, 0, 0, 0, 0, 1).

Crossrefs

Cf. A041427, A041018, A041046, A041090, A041150, A041226, A041318, A041426, A041550.

Programs

Mathematica

Numerator[Convergents[Sqrt[229], 30]] (* Vincenzo Librandi, Nov 01 2013 *)
LinearRecurrence[{0,0,0,0,3420,0,0,0,0,1},{15,106,121,227,1710,51527,362399,413926,776325,5848201},30] (* Harvey P. Dale, Dec 19 2016 *)

Formula

From Johannes W. Meijer, Jun 12 2010: (Start)

a(5n) = A090301(3n+1), a(5n+1) = (A090301(3n+2) - A090301(3n+1))/2, a(5n+2) = (A090301(3n+2) + A090301(3n+1))/2, a(5n+3) = A090301(3n+2) and a(5n+4) = A090301(3n+3)/2. (End)

G.f.: -(x^9-15*x^8+106*x^7-121*x^6+227*x^5+1710*x^4+227*x^3+121*x^2+106*x+15) / (x^10+3420*x^5-1). - Colin Barker, Nov 08 2013

Extensions

More terms from Colin Barker, Nov 08 2013