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

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Mathematica

Min[ContinuedFraction[Sqrt[#]][[2]]]&/@Select[Range[ 200], !IntegerQ[ Sqrt[ #]]&] (* Harvey P. Dale, May 20 2021 *)

Prog

(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

Crossrefs

Cf. A276689, A000037.

Sequence in context: A007739 A330086 A290935 * A013942 A187816 A088423

Adjacent sequences: A031421 A031422 A031423 * A031425 A031426 A031427

Keyword

nonn

Author

David W. Wilson

Extensions

Name corrected by Charles R Greathouse IV, Aug 10 2017

Status

approved