OFFSET
1,1
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 1..248
EXAMPLE
The fundamental unit of Z[sqrt(2)] is 1 + sqrt(2) = 2.414213562373...
The fundamental unit of Z[sqrt(3)] is 2 + sqrt(3) = 3.7320508..., which is larger than 2.414213562373...
Thus the sequence starts out 2, 3.
The fundamental unit of O_(Q(sqrt(5))) is 1/2 + sqrt(5)/2 = 1.618..., which is actually smaller than the previous units, so 5 is not in the sequence.
The next term in the sequence is 6, corresponding to 5 + 2 sqrt(6) = 9.8989794855663561963945681494...
MATHEMATICA
k = 2; A294176 = {}; mx = 0; While[k < 1000, If[SquareFreeQ@ k && N[NumberFieldFundamentalUnits[Sqrt[k]], 16][[1]] > mx, mx = N[NumberFieldFundamentalUnits[Sqrt[k]], 16][[1]]; AppendTo[A294176, k]]; k++]; A294176 (* Robert G. Wilson v, Feb 11 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alonso del Arte, Feb 10 2018
EXTENSIONS
a(10) onward from Robert G. Wilson v, Feb 11 2018
STATUS
approved