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A333640
Numbers k such that the continued fraction of (1 + sqrt(k))/2 has period 13.
3
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
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 &]
KEYWORD
nonn
AUTHOR
Amiram Eldar, Mar 31 2020
STATUS
approved