A041100 Numerators of continued fraction convergents to sqrt(58).

7, 8, 15, 23, 38, 61, 99, 1447, 1546, 2993, 4539, 7532, 12071, 19603, 286513, 306116, 592629, 898745, 1491374, 2390119, 3881493, 56731021, 60612514, 117343535, 177956049, 295299584, 473255633, 768555217, 11233028671, 12001583888, 23234612559, 35236196447

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Kristina Lund, Steven Schlicker and Patrick Sigmon, Fibonacci sequences and the space of compact sets, Involve, 1:2 (2008), pp. 159-165.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,198,0,0,0,0,0,0,1).

Formula

G.f.: -(x^13 -7*x^12 +8*x^11 -15*x^10 +23*x^9 -38*x^8 +61*x^7 +99*x^6 +61*x^5 +38*x^4 +23*x^3 +15*x^2 +8*x +7) / (x^14 +198*x^7 -1). - Colin Barker, Nov 08 2013

Maple

cf:=numtheory:-cfrac(sqrt(58), 100):
seq(numtheory:-nthnumer(cf, n), n=0..100); # Robert Israel, Sep 02 2015

Mathematica

Numerator[Convergents[Sqrt[58], 30]] (* Vincenzo Librandi, Oct 29 2013 *)

Crossrefs

Cf. A041101, A010511.

Sequence in context: A231458 A070424 A022097 * A129658 A041693 A042001

Adjacent sequences: A041097 A041098 A041099 * A041101 A041102 A041103

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 08 2013

Status

approved