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%I #34 Sep 22 2022 01:49:25
%S 5,7,9,10,14,17,18,20,23,28,33,34,36,40,46,56,65,66,68,72,80,92,112,
%T 129,130,132,136,144,160,184,224,257,258,260,264,272,288,320,368,448,
%U 513,514,516,520,528,544,576,640,736,896,1025,1026,1028,1032,1040
%N Numbers whose squares are the sum of exactly three distinct powers of 2.
%C The finite sequence 5, 7, 9, 10, 14, 17 arises in the following context: squarefree circular words over the ternary alphabet exist for all lengths n except for 5, 7, 9, 10, 14, 17. See Currie (2002), Shur (2010). - _N. J. A. Sloane_, May 04 2013
%H Giovanni Resta, <a href="/A212191/b212191.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Reinhard Zumkeller)
%H J. D. Currie, <a href="https://doi.org/10.37236/1671">There are ternary circular square-free words of length n for n >= 18</a>, Elect. J. Combinatorics 9 (2002), Note #N10.
%H James D. Currie, and Jesse T. Johnson, <a href="https://arxiv.org/abs/2005.06235">There are level ternary circular square-free words of length n for n != 5,7,9,10,14,17</a>, arXiv:2005.06235 [math.CO], 2020.
%H Arseny M. Shur, <a href="https://doi.org/10.37236/412">On Ternary Square-free Circular Words</a>, Electronic J. Combin., Volume 17 (2010), Research Paper #R140.
%F a(n)^2 = A212190(n).
%t Select[Range[1, 1000], Total[IntegerDigits[#^2, 2]] == 3 &] (* _T. D. Noe_, Dec 07 2012 *)
%o (Haskell)
%o a212191 n = a212191_list !! (n-1)
%o a212191_list = map a000196 a212190_list
%Y Cf. A000196, A005009 (subsequence).
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, May 03 2012