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A096491
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a(n) = sqrt(n) of n if n is a perfect square, otherwise a(n) = largest term in period of continued fraction expansion of square root of n.
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7
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1, 2, 2, 2, 4, 4, 4, 4, 3, 6, 6, 6, 6, 6, 6, 4, 8, 8, 8, 8, 8, 8, 8, 8, 5, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 6, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 7, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 8, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16
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OFFSET
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1,2
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LINKS
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EXAMPLE
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For n=127: the period={3,1,2,2,7,11,7,2,2,1,3,22}, max=a(127)=22.
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MAPLE
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if issqr(n) then
sqrt(n) ;
else
numtheory[cfrac](sqrt(n), 'periodic', 'quotients') ;
%[2] ;
max(op(%)) ;
end if;
end proc:
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MATHEMATICA
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u=1; Do[s=Max[Last[ContinuedFraction[n^(1/2)]]]; tc[[u]]=s; u=u+1, {n, 1, m}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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