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A197128 Nonsquare positive integers n such that the fundamental unit of quadratic field Q(sqrt(n))is not singular. 5
2, 3, 5, 7, 8, 10, 11, 12, 13, 15, 17, 18, 19, 20, 21, 23, 24, 26, 27, 28, 29, 31, 32, 33, 35, 37, 39, 40, 41, 43, 44, 45, 47, 48, 50, 51, 52, 53, 55, 57, 58, 59, 60, 61, 63, 65, 67, 68, 71, 72, 73, 74, 75, 76, 77, 79, 80, 82, 83, 84, 85, 88, 89, 90, 91, 92 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

x^2+n*y^2=(+/-)2^s where s is 0 or 1.

Definition: Unity is singular when GCD[n,y]<>1.

LINKS

Table of n, a(n) for n=1..66.

MATHEMATICA

cr = {}; Do[If[IntegerQ[Sqrt[n]], , kk = NumberFieldFundamentalUnits[Sqrt[n]]; d1 = kk[[1]][[2]][[1]]; d2 = kk[[1]][[1]] kk[[1]][[2]][[2]]; d4 = Numerator[d2/Sqrt[n]]; If[GCD[d4, n] == 1, AppendTo[cr, n]]], {n, 2, 330}]; cr

CROSSREFS

Cf. A087643, A172000, A194366, A197115, A197127.

Sequence in context: A302293 A266347 A028788 * A034707 A288378 A187909

Adjacent sequences:  A197125 A197126 A197127 * A197129 A197130 A197131

KEYWORD

nonn

AUTHOR

Artur Jasinski, Oct 10 2011

STATUS

approved

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Last modified February 19 22:36 EST 2020. Contains 332061 sequences. (Running on oeis4.)