

A172000


Nonsquare positive integers n such that the fundamental unit of quadratic field Q(sqrt(n)) has norm 1.


18



2, 5, 8, 10, 13, 17, 18, 20, 26, 29, 32, 37, 40, 41, 45, 50, 52, 53, 58, 61, 65, 68, 72, 73, 74, 80, 82, 85, 89, 90, 97, 98, 101, 104, 106, 109, 113, 116, 117, 122, 125, 128, 130, 137, 145, 148, 149, 153, 157, 160, 162, 164, 170, 173, 180, 181, 185, 193, 197, 200
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OFFSET

1,1


COMMENTS

Contains A003814 as a subsequence, their squarefree terms coincide and form A003654.
It seems that this sequence also gives the values of n such that the equation x^2  n*y^2 = n has integer solutions.  Colin Barker, Aug 20 2013


LINKS



FORMULA

A positive integer n is in this sequence iff its squarefree core A007913(n) belongs to A003654.


MATHEMATICA

cr = {}; Do[If[IntegerQ[Sqrt[n]], , kk = NumberFieldFundamentalUnits[Sqrt[n]]; d1 = kk[[1]][[2]][[1]]; d2 = kk[[1]][[1]] kk[[1]][[2]][[2]]; d3 = Expand[(d1 + d2) (d1  d2)]; If[d3 == 1, AppendTo[cr, n]]], {n, 2, 1000}]; cr (* Artur Jasinski, Oct 10 2011 *)


PROG

(PARI) { for(n=1, 1000, if(issquare(n), next); if( norm(bnfinit(x^2n).fu[1])==1, print1(n, ", ")) ) }


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



