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A096485 Period length of continued fraction for square root of n-th decimal repunit. 3
2, 6, 2, 24, 2, 622, 2, 2396, 2, 21912, 2, 527718, 2, 168484, 2, 13171730, 2, 359947864, 2, 52090778, 2, 16658818532, 2, 134257065348, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

LINKS

Table of n, a(n) for n=2..26.

EXAMPLE

n=10: the period is [3,66666];

n=3: the period is [2, 2, 4, 5, 2, 7, 1, 41, 3, 1, 1, 4, 1, 1, 3, 41, 1, 7, 2, 5, 4, 2, 2, 210], 24 terms.

MAPLE

A096485 := proc(n) ((10^n-1)/9)^(1/2) ; nops(numtheory[cfrac](%, 'periodic', 'quotients')[2]) ; end: for n from 2 to 10 do print(A096485(n)) ; od ; # R. J. Mathar, Apr 30 2007

with(numtheory): [seq(nops(cfrac(((10^k-1/9)^(1/2), 'periodic', 'quotients')[2]), k=2..10)];

MATHEMATICA

Do[Print[Length[Last[ContinuedFraction[((-1+10^n)/9)^(1/2)]]]], {n, 2, 18}]

CROSSREFS

Cf. A002275, A096483, A096484.

Sequence in context: A254638 A320118 A320016 * A125032 A076743 A131980

Adjacent sequences:  A096482 A096483 A096484 * A096486 A096487 A096488

KEYWORD

more,nonn,base

AUTHOR

Labos Elemer, Jun 24 2004

EXTENSIONS

a(19)-a(26) from Hiroaki Yamanouchi, Oct 17 2015

STATUS

approved

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Last modified April 5 06:13 EDT 2020. Contains 333238 sequences. (Running on oeis4.)