A064025 Length of period of the continued fraction for sqrt(n!).

1, 2, 2, 2, 4, 2, 16, 48, 8, 4, 56, 180, 44, 156, 300, 7936, 10388, 11516, 9104, 13469268, 2684084, 2418800, 28468692, 143007944, 85509116, 402570696, 2287868888, 204306960, 48715166536, 147160740856, 317585614148

Offset: 2

Author

Labos Elemer, Sep 18 2001

Keywords

• nonn
• more

Examples

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

Crossrefs

Cf. A000142, A003285.

Programs

Maple

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

Mathematica

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

Formula

a(n) = A003285(A000142(n)). - Michel Marcus, Sep 25 2019

Extensions

More terms from Robert G. Wilson v, Oct 01 2001

a(25)-a(28) from Daniel Suteu, Jan 24 2019

a(29) from Chai Wah Wu, Sep 23 2019

a(30) from Chai Wah Wu, Sep 25 2019

a(31) from Chai Wah Wu, Jan 27 2021

a(32) from Chai Wah Wu, Feb 02 2021