A041190 Numerators of continued fraction convergents to sqrt(106).

10, 31, 72, 103, 175, 278, 453, 1184, 4005, 81284, 247857, 576998, 824855, 1401853, 2226708, 3628561, 9483830, 32080051, 651084850, 1985334601, 4621754052, 6607088653, 11228842705, 17835931358, 29064774063, 75965479484, 256961212515, 5215189729784

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,8010,0,0,0,0,0,0,0,0,1).

Formula

G.f.: -(x^17 -10*x^16 +31*x^15 -72*x^14 +103*x^13 -175*x^12 +278*x^11 -453*x^10 +1184*x^9 +4005*x^8 +1184*x^7 +453*x^6 +278*x^5 +175*x^4 +103*x^3 +72*x^2 +31*x +10) / (x^18 +8010*x^9 -1). - Colin Barker, Nov 08 2013

Mathematica

Numerator[Convergents[Sqrt[106], 30]] (* Vincenzo Librandi, Oct 30 2013 *)

Prog

(Python)
from sympy import sqrt
from sympy.ntheory.continued_fraction import *
def aupton(terms):
  g = continued_fraction_convergents(continued_fraction_iterator(sqrt(106)))
  return [next(g).numerator() for n in range(terms)]
print(aupton(28)) # Michael S. Branicky, Oct 31 2021

Crossrefs

Cf. A041191, A010172.

Sequence in context: A219693 A297507 A163655 * A111500 A342362 A161325

Adjacent sequences: A041187 A041188 A041189 * A041191 A041192 A041193

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 08 2013

Status

approved