A146336 Numbers k such that continued fraction of (1 + sqrt(k))/2 has period 12.

94, 103, 124, 127, 128, 158, 160, 177, 190, 204, 208, 209, 216, 236, 239, 247, 263, 295, 296, 302, 316, 332, 351, 364, 376, 384, 385, 415, 423, 426, 432, 460, 464, 479, 492, 535, 544, 585, 606, 608, 609, 636, 639, 666, 668, 684, 696, 706, 734, 736, 744, 750

Offset: 1

Author

Artur Jasinski, Oct 30 2008

Keywords

• nonn

Comments

For primes in this sequence see A146357.

Examples

			a(2) = 103 because continued fraction of (1+sqrt(103))/2 = 15, 1, 1, 2, 1, 6, 20, 6, 1, 2, 1, 1, 9, 1, 1, 2, 1, 6, 20, 6, 1, 2, 1, 1, 9, 1, 1, 2, 1, 6, 20, 6, 1, 2 ... has period (1, 1, 2, 1, 6, 20, 6, 1, 2, 1, 1, 9) length 12.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Crossrefs

Cf. A000290, A078370, A146326-A146345, A146348-A146360.

Programs

Mathematica

cf12Q[n_]:=!OddQ[Sqrt[n]]&&Length[ContinuedFraction[(1+Sqrt[n])/2][[2]]]==12; Select[Range[800],cf12Q] (* Harvey P. Dale, Oct 15 2011 *)