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Length of period of the continued fraction for sqrt(n!).
2

%I #28 Feb 02 2021 20:07:16

%S 1,2,2,2,4,2,16,48,8,4,56,180,44,156,300,7936,10388,11516,9104,

%T 13469268,2684084,2418800,28468692,143007944,85509116,402570696,

%U 2287868888,204306960,48715166536,147160740856,317585614148

%N Length of period of the continued fraction for sqrt(n!).

%F a(n) = A003285(A000142(n)). - _Michel Marcus_, Sep 25 2019

%e Quotients for 10! are [[1904], [1, 15, 1, 13, 1, 15, 1, 3808]], so period length of 10! is 8.

%p with(numtheory): [seq(nops(cfrac(sqrt(k!),'periodic','quotients')[2]),k=2..16)];

%t Do[ Print[ Length[ Last[ ContinuedFraction[ Sqrt[ n! ]]]]], {n, 2, 24} ]

%Y Cf. A000142, A003285.

%K nonn,more

%O 2,2

%A _Labos Elemer_, Sep 18 2001

%E More terms from _Robert G. Wilson v_, Oct 01 2001

%E a(25)-a(28) from _Daniel Suteu_, Jan 24 2019

%E a(29) from _Chai Wah Wu_, Sep 23 2019

%E a(30) from _Chai Wah Wu_, Sep 25 2019

%E a(31) from _Chai Wah Wu_, Jan 27 2021

%E a(32) from _Chai Wah Wu_, Feb 02 2021