This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
Z:=PolynomialRing(Integers()); N :=NumberField(2*x^2-2*x-1); S:=[ r^n+(1-r)^n: n in [1..300] ]; [ k: j in [1..#S] | IsPrime(k) where k is Numerator(RationalField()!S[j])];
a(3) = 2 because x^3 + y^3 = 5/2.
nmax:=45: f:=n-> coeftayl((1+x)/(1-2*x-11*x^2-6*x^3), x=-1, n): a(1):=1: for n from 0 to nmax do a(n+2):= denom(f(n)) od: seq(a(n),n=1..nmax); # Johannes W. Meijer, Aug 16 2010
Denominator[Map[First, NestList[{Last[#], Last[#] + First[#]/2} &, {1, 2}, 50]]] (* Paolo Xausa, Feb 01 2024, after Nick Hobson *)
a(n) = denominator(2*polcoeff( lift( Mod((1+x)/2,x^2-3)^n ), 0)) \\ Max Alekseyev, Feb 23 2010
from fractions import Fraction
def a173300_gen(a, b):
while True:
yield a.denominator
b, a = b + Fraction(a, 2), b
for n, a_n in zip(range(1, 47), a173300_gen(1, 2)):
print(n, a_n) # Nick Hobson, Jan 30 2024
Table[Numerator[Simplify[((1/2 (Sqrt[3] + 1))^x - (1/2 (Sqrt[3] - 1))^x Cos[Pi x])/Sqrt[3]]], {x, 0, 36}]
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