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A064025 Length of period of the continued fraction for sqrt(n!). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

LINKS

Table of n, a(n) for n=2..32.

FORMULA

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

EXAMPLE

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

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} ]

CROSSREFS

Cf. A000142, A003285.

Sequence in context: A135293 A216951 A320305 * A182154 A273875 A054709

Adjacent sequences:  A064022 A064023 A064024 * A064026 A064027 A064028

KEYWORD

nonn,more

AUTHOR

Labos Elemer, Sep 18 2001

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

STATUS

approved

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Last modified May 14 07:13 EDT 2021. Contains 343879 sequences. (Running on oeis4.)