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 A087643 Nonsquare positive integers n such that the fundamental unit of quadratic field Q(sqrt(n)) has norm 1. 13
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 19 02:20 EDT 2024. Contains 376003 sequences. (Running on oeis4.)