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

1,1

Comments

For primes in this sequence see A146358.

Links

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

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A051648 A375407 A217497 * A146358 A050962 A020376

Adjacent sequences: A333637 A333638 A333639 * A333641 A333642 A333643

Keyword

nonn

Author

Amiram Eldar, Mar 31 2020

Status

approved