A041226 Numerators of continued fraction convergents to sqrt(125).

11, 56, 67, 123, 682, 15127, 76317, 91444, 167761, 930249, 20633239, 104096444, 124729683, 228826127, 1268860318, 28143753123, 141987625933, 170131379056, 312119004989, 1730726404001, 38388099893011, 193671225869056, 232059325762067, 425730551631123

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• 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 A001946.

For the terms of the periodical sequence of the continued fraction for sqrt(125) see A010186. 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 (0,0,0,0,1364,0,0,0,0,1).

Crossrefs

Cf. A041227, A041018, A041046, A041090, A041150, A041226, A041318, A041426, A041550.

Programs

Mathematica

Numerator[Convergents[Sqrt[125], 30]] (* Vincenzo Librandi, Oct 31 2013 *)

Formula

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

a(5n) = A001946(3n+1),

a(5n+1) = (A001946(3n+2) - A001946(3n+1))/2,

a(5n+2) = (A001946(3n+2) + A001946(3n+1))/2,

a(5n+3) = A001946(3n+2),

a(5n+4) = A001946(3n+3)/2. (End)

G.f.: -(x^9 -11*x^8 +56*x^7 -67*x^6 +123*x^5 +682*x^4 +123*x^3 +67*x^2 +56*x +11) / ((x^2 +4*x -1)*(x^4 -7*x^3 +19*x^2 -3*x +1)*(x^4 +3*x^3 +19*x^2 +7*x +1)). - Colin Barker, Nov 08 2013

Extensions

More terms from Colin Barker, Nov 08 2013