A031424 Least term in period of continued fraction for sqrt(n), as n runs through the nonsquares (A000037).
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
Offset: 1
Keywords
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
Min[ContinuedFraction[Sqrt[#]][[2]]]&/@Select[Range[ 200],!IntegerQ[ Sqrt[ #]]&] (* Harvey P. Dale, May 20 2021 *)
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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
Extensions
Name corrected by Charles R Greathouse IV, Aug 10 2017