A294176 Squarefree d such that the fundamental unit of Q(sqrt(d)) is larger than the fundamental unit of Q(sqrt(d)) for any smaller d.

2, 3, 6, 7, 11, 14, 19, 22, 31, 43, 46, 67, 94, 127, 139, 151, 199, 211, 214, 331, 379, 454, 526, 571, 631, 739, 751, 886, 919, 991, 1291, 1366, 1699, 1726, 1999, 2011, 2311, 2326, 2566, 2671, 3019, 3259, 3691, 3931, 4174, 4846, 4951, 5119, 6211, 6379, 6406, 6451, 7606, 8254, 8779, 9619

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

Cf. A014000, A014046.

Sequence in context: A323066 A002256 A230584 * A008765 A018468 A117115

Adjacent sequences: A294173 A294174 A294175 * A294177 A294178 A294179

Keyword

nonn

Author

Alonso del Arte, Feb 10 2018

Extensions

a(10) onward from Robert G. Wilson v, Feb 11 2018

Status

approved