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

Author

Alonso del Arte, Feb 10 2018

Keywords

• nonn

Examples

			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...
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..248

Crossrefs

Cf. A014000, A014046.

Programs

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 *)

Extensions

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