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

8, 125, 216, 1728

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..4.

Mathematica

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

Prog

(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
isok(m) = f(m)^3 == m; \\ Michel Marcus, Jul 12 2021

Crossrefs

Cf. A003285.

Sequence in context: A024282 A340888 A231638 * A053058 A050803 A016791

Adjacent sequences: A065079 A065080 A065081 * A065083 A065084 A065085

Keyword

nonn,more

Author

Naohiro Nomoto, Nov 09 2001

Status

approved