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Length of period of continued fraction for square root of 1+n!.
1

%I #29 Oct 02 2019 01:35:48

%S 1,2,4,0,0,40,0,153,558,3074,4285,22602,180544,766146,766082,524570,

%T 9932193,5193268,763601450,4284694240,3059999982,48742214702,

%U 6354126960,1975806716944,929707144775

%N Length of period of continued fraction for square root of 1+n!.

%F a(n) = A003285(A038507(n)). - _Michel Marcus_, Sep 25 2019

%e Period for sqrt(3!+1) = sqrt(7) = {1,1,1,4}, a(3) = 4.

%t Table[Length[Last[ContinuedFraction[Sqrt[1+n! ]]]], {n, 1, 14}]

%Y Cf. A003285, A038507, A078146, A064025.

%K nonn,hard,more

%O 1,2

%A _Labos Elemer_, Nov 25 2002

%E a(15)-a(20) from _Vaclav Kotesovec_, Aug 28 2019

%E a(21) from _Chai Wah Wu_, Sep 23 2019

%E a(22)-a(23) from _Chai Wah Wu_, Sep 25 2019

%E a(24)-a(25) from _Chai Wah Wu_, Oct 01 2019