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 A065082 Numbers k such that (period of the continued fraction for sqrt(k))^3 = k. 0

%I #14 Jul 13 2021 06:23:58

%S 8,125,216,1728

%N Numbers k such that (period of the continued fraction for sqrt(k))^3 = k.

%C Next term, if it exists, exceeds 6600000. - Sam Handler (sam_5_5_5_0(AT)yahoo.com), Nov 14 2004

%t Do[ If[ Length[ Last[ ContinuedFraction[ Sqrt[n]]]]^3 == n, Print[n]], {n, 1, 10^5} ]

%o (PARI) f(n) = {if (issquare(n), 0, my(p=100); while (! isokq(n, p), p+=100); localprec(p); my(cf = contfrac(sqrt(n))); for (k=2, #cf, if (cf[k] == 2*cf[1], return (k-1))););} \\ A003285

%o isok(m) = f(m)^3 == m; \\ _Michel Marcus_, Jul 12 2021

%Y Cf. A003285.

%K nonn,more

%O 1,1

%A _Naohiro Nomoto_, Nov 09 2001

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Last modified December 7 01:11 EST 2023. Contains 367616 sequences. (Running on oeis4.)