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Numerators of continued fraction convergents to sqrt(106).
2

%I #20 Nov 01 2021 03:28:22

%S 10,31,72,103,175,278,453,1184,4005,81284,247857,576998,824855,

%T 1401853,2226708,3628561,9483830,32080051,651084850,1985334601,

%U 4621754052,6607088653,11228842705,17835931358,29064774063,75965479484,256961212515,5215189729784

%N Numerators of continued fraction convergents to sqrt(106).

%H Vincenzo Librandi, <a href="/A041190/b041190.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,8010,0,0,0,0,0,0,0,0,1).

%F 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

%t Numerator[Convergents[Sqrt[106], 30]] (* _Vincenzo Librandi_, Oct 30 2013 *)

%o (Python)

%o from sympy import sqrt

%o from sympy.ntheory.continued_fraction import *

%o def aupton(terms):

%o g = continued_fraction_convergents(continued_fraction_iterator(sqrt(106)))

%o return [next(g).numerator() for n in range(terms)]

%o print(aupton(28)) # _Michael S. Branicky_, Oct 31 2021

%Y Cf. A041191, A010172.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 08 2013