A333640 Numbers k such that the continued fraction of (1 + sqrt(k))/2 has period 13.

421, 757, 1021, 1097, 1117, 1241, 1301, 1553, 1625, 1649, 1973, 2069, 2125, 2237, 2249, 2273, 2665, 2789, 2861, 3085, 3349, 3373, 3461, 3517, 3545, 3877, 3917, 4133, 4397, 4481, 4573, 4589, 4885, 5389, 5521, 5573, 5713, 5717, 6185, 6221, 6317, 6637, 6997, 7093

Offset: 1

Author

Amiram Eldar, Mar 31 2020

Keywords

• nonn

Comments

For primes in this sequence see A146358.

Examples

			a(1) = 421 because the continued fraction of (1 + sqrt(421))/2 = 10, 1, 3, 6, 1, 1, 2, 2, 1, 1, 6, 3, 1, 19, 1, 3, 6, ... has a period (1, 3, 6, 1, 1, 2, 2, 1, 1, 6, 3, 1, 19) of length 13.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000290, A078370, A146326-A146345, A146348-A146362.

Programs

Mathematica

Select[Range[10^4], !IntegerQ @ Sqrt[#] && Length[ContinuedFraction[(1 + Sqrt[#])/2][[2]]] == 13 &]