A087643 - OEIS

A087643

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

3, 6, 7, 11, 12, 14, 15, 19, 21, 22, 23, 24, 27, 28, 30, 31, 33, 34, 35, 38, 39, 42, 43, 44, 46, 47, 48, 51, 54, 55, 56, 57, 59, 60, 62, 63, 66, 67, 69, 70, 71, 75, 76, 77, 78, 79, 83, 84, 86, 87, 88, 91, 92, 93, 94, 95, 96, 99, 102, 103, 105, 107, 108, 110, 111, 112, 114

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OFFSET

3,1

COMMENTS

No quadratic number with a fully periodical continued fraction of period 1 can be written as (a+b*sqrt(n))/c with n allowed to have square factors.

Subsequence of the squarefree terms is A087642.

LINKS

Table of n, a(n) for n=3..69.

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 *)

CROSSREFS

Cf. A087642, A172000.

Sequence in context: A051146 A136272 A101184 * A248150 A022544 A194366

Adjacent sequences: A087640 A087641 A087642 * A087644 A087645 A087646

KEYWORD

easy,nonn

AUTHOR

Thomas Baruchel, Sep 16 2003

EXTENSIONS

Edited by Max Alekseyev, May 03 2010

STATUS

approved