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A369346
Continued fraction expansion of the real root of x^3 - x^2 - 1 = 0.
1
1, 2, 6, 1, 3, 5, 4, 22, 1, 1, 4, 1, 2, 84, 1, 3, 1, 6, 1, 3, 1, 9, 1, 1, 1, 1, 19, 3, 1, 2, 1, 5, 1, 5, 2, 2, 1, 1, 1, 1, 76, 6, 8, 1, 1, 5, 1, 5, 1, 1, 25, 1, 2, 1, 116, 2, 1, 8, 1, 1, 3, 1, 53, 5, 276, 2, 1, 1, 1, 3, 3, 2, 1, 1, 4, 13, 1, 1, 1, 4, 1, 1, 1, 9, 9, 1, 1, 9, 6, 1, 2, 32
OFFSET
1,2
LINKS
MATHEMATICA
ContinuedFraction[x/.First[Solve[x^3-x^2-1==0, x]], 92] (* Stefano Spezia, Jan 21 2024 *)
PROG
(bc)
/* The "test" calculation evaluates the cubic to confirm the calculation of the root. */
define iter(frac)
{j = 0
while(frac > 1){
frac -= 1;
j+=1}
j
return 1/frac}
scale=12578
f=(1+(e(l(((29+3*sqrt(93))/2))/3))+(e(l(((29-3*sqrt(93))/2))/3)))/3
psi=f
test=(psi-1)*psi*psi-1
for(i=0; i<12175; i++)f=iter(f)
(PARI)
\p100 \\ realprecision
contfrac(solve(x = 1, 2, x^3 - x^2 - 1), , 80) \\ Hugo Pfoertner, Jan 21 2024
CROSSREFS
Cf. A092526 (decimal expansion).
Sequence in context: A269224 A257240 A121601 * A355929 A122761 A100469
KEYWORD
nonn,cofr
AUTHOR
Patrick McKinley, Jan 20 2024
STATUS
approved