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A197127 Nonsquare positive integers n such that the fundamental unit of quadratic field Q(sqrt(d))is singular. 5
6, 14, 22, 30, 34, 38, 42, 46, 54, 56, 62, 66, 69, 70, 78, 86, 87, 93, 94, 102, 110, 114, 115, 118, 126, 130, 132, 134, 138, 142, 146, 150, 154, 155, 156, 158, 159, 166, 174, 177, 178, 182, 183, 184, 185, 186, 190, 194, 198, 206, 210, 214, 220, 222, 228, 230 (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..56.

EXAMPLE

a(1)=6 because unity of quadratic field  Q(6) is 5+2*Sqrt[6] and GCD[2,6]=2 <>1.

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 (*Artur Jasinski*)

CROSSREFS

Cf. A087643, A172000, A194366, A197115, A197128.

Sequence in context: A195063 A138290 A023057 * A197171 A062316 A079299

Adjacent sequences:  A197124 A197125 A197126 * A197128 A197129 A197130

KEYWORD

nonn

AUTHOR

Artur Jasinski, Oct 10 2011

STATUS

approved

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Last modified February 27 09:44 EST 2020. Contains 332301 sequences. (Running on oeis4.)