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A333640 Numbers k such that the continued fraction of (1 + sqrt(k))/2 has period 13. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A268859 A051648 A217497 * A146358 A050962 A020376

Adjacent sequences:  A333637 A333638 A333639 * A333641 A333642 A333643

KEYWORD

nonn

AUTHOR

Amiram Eldar, Mar 31 2020

STATUS

approved

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Last modified September 26 01:25 EDT 2020. Contains 337346 sequences. (Running on oeis4.)