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A096494
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Largest value in period of continued fraction of square root of n-th prime.
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1
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2, 2, 4, 4, 6, 6, 8, 8, 8, 10, 10, 12, 12, 12, 12, 14, 14, 14, 16, 16, 16, 16, 18, 18, 18, 20, 20, 20, 20, 20, 22, 22, 22, 22, 24, 24, 24, 24, 24, 26, 26, 26, 26, 26, 28, 28, 28, 28, 30, 30, 30, 30, 30, 30, 32, 32, 32, 32, 32, 32, 32, 34, 34, 34, 34, 34, 36, 36, 36, 36, 36, 36
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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FORMULA
| It seems that limit n ->infinity a(n)/n = 0. - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 19 2003
a(n)=2*A000006(n). - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 19 2003
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EXAMPLE
| n=31,p[31]=127: the period={3,1,2,2,7,11,7,2,2,1,3,22},a[31]=22;
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MAPLE
| (Maple code from R. J. Mathar, Mar 18 2010)
A096491 := proc(n)
if issqr(n) then
sqrt(n) ;
else
numtheory[cfrac](sqrt(n), 'periodic', 'quotients') ;
%[2] ;
max(op(%)) ;
end if;
end proc:
A096494 := proc(n)
option remember ;
A096491(ithprime(n)) ;
end proc:
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MATHEMATICA
| {te=Table[0, {m}], u=1}; Do[s=Max[Last[ContinuedFraction[Prime[n]^(1/2)]]]; te[[u]]=s; u=u+1, {n, 1, m}]; te
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CROSSREFS
| Cf. A003285, A054269, A005980, A096491-A096496.
Sequence in context: A079584 A179291 A004079 * A116568 A061106 A161764
Adjacent sequences: A096491 A096492 A096493 * A096495 A096496 A096497
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Jun 29 2004
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