A197171 Values k such that singular quadratic unity of Q(k) have gcd(k,y) = 2.

6, 14, 22, 30, 34, 38, 42, 54, 56, 62, 66, 86, 94, 102, 110, 118, 126, 132, 134, 138, 142, 146, 150, 156, 158, 166, 174, 178, 182, 186, 190, 194, 198, 206, 210, 214, 220, 222, 228, 230, 246, 254, 258, 262, 270, 278, 282, 286, 294, 302, 306, 310, 322, 326

Offset

2,1

Comments

Conjecture: This sequence is infinite.

Links

Table of n, a(n) for n=2..55.

Mathematica

cr = {}; ck = {}; 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[ck, GCD[d4, n]]; AppendTo[cr, n]]], {n, 2, 200000}]; aa = {}; Do[If[ck[[n]] == 2, AppendTo[aa, cr[[n]]]], {n, 1, Length[cr]}]; aa

Crossrefs

Cf. A087643, A172000, A194366, A197115, A197127, A197128, A197170.

Sequence in context: A138290 A023057 A197127 * A062316 A079299 A043445

Adjacent sequences: A197168 A197169 A197170 * A197172 A197173 A197174

Keyword

nonn

Author

Artur Jasinski, Oct 11 2011

Status

approved