login
A041190
Numerators of continued fraction convergents to sqrt(106).
2
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
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
Sequence in context: A219693 A297507 A163655 * A111500 A342362 A161325
KEYWORD
nonn,cofr,frac,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Nov 08 2013
STATUS
approved