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A369346 Continued fraction expansion of the real root of x^3 - x^2 - 1 = 0.

%I A369346 #35 Feb 14 2025 17:27:04
%S A369346 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,
%T A369346 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,
%U A369346 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
%N A369346 Continued fraction expansion of the real root of x^3 - x^2 - 1 = 0.
%H A369346 Patrick McKinley, <a href="/A369346/b369346.txt">Table of n, a(n) for n = 0..12174</a>
%H A369346 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SupergoldenRatio.html">Supergolden Ratio</a>.
%t A369346 ContinuedFraction[x/.First[Solve[x^3-x^2-1==0,x]],92] (* _Stefano Spezia_, Jan 21 2024 *)
%o A369346 (bc)
%o A369346 /* The "test" calculation evaluates the cubic to confirm the calculation of the root. */
%o A369346 define iter(frac)
%o A369346 {j = 0
%o A369346  while(frac > 1){
%o A369346    frac -= 1;
%o A369346    j+=1}
%o A369346  j
%o A369346  return 1/frac}
%o A369346 scale=12578
%o A369346 f=(1+(e(l(((29+3*sqrt(93))/2))/3))+(e(l(((29-3*sqrt(93))/2))/3)))/3
%o A369346 psi=f
%o A369346 test=(psi-1)*psi*psi-1
%o A369346 for(i=0;i<12175;i++)f=iter(f)
%o A369346 (PARI)
%o A369346 \p100 \\ realprecision
%o A369346 contfrac(solve(x = 1, 2, x^3 - x^2 - 1),, 80) \\ _Hugo Pfoertner_, Jan 21 2024
%Y A369346 Cf. A092526 (decimal expansion), A381124, A381125 (convergents).
%K A369346 nonn,cofr
%O A369346 0,2
%A A369346 _Patrick McKinley_, Jan 20 2024
%E A369346 Offset changed by _Andrew Howroyd_, Feb 14 2025