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A031424
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Least term in period of continued fraction for sqrt(n), as n runs through the nonsquares (A000037).
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7
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2, 1, 4, 2, 1, 1, 6, 3, 2, 1, 1, 1, 8, 4, 1, 2, 1, 1, 1, 1, 10, 5, 2, 1, 2, 1, 1, 1, 1, 1, 12, 6, 4, 3, 2, 2, 1, 1, 1, 1, 1, 1, 14, 7, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 16, 8, 1, 4, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 18, 9, 6, 1, 1, 3, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 20, 10, 1, 5, 4, 1
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OFFSET
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1,1
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LINKS
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MATHEMATICA
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Min[ContinuedFraction[Sqrt[#]][[2]]]&/@Select[Range[ 200], !IntegerQ[ Sqrt[ #]]&] (* Harvey P. Dale, May 20 2021 *)
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PROG
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(PARI) do(n)=my(a0=sqrtint(n), a, b=a0, c=n-a0^2, bold, cold, least=2*a0); while(1, a=(a0+b)\c; if(a<2, return(1)); least=min(least, a); bold=b; b=a*c-b; cold=c; c=(n-b^2)\c; if(b==bold || c==cold, return(least)))
first(n)=my(v=vector(n), k, i); while(1, k++; for(m=k^2+1, k^2+2*k, if(i++>n, return(v)); v[i]=do(m))) \\ Charles R Greathouse IV, Aug 10 2017
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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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