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A212191
Numbers whose squares are the sum of exactly three distinct powers of 2.
4
5, 7, 9, 10, 14, 17, 18, 20, 23, 28, 33, 34, 36, 40, 46, 56, 65, 66, 68, 72, 80, 92, 112, 129, 130, 132, 136, 144, 160, 184, 224, 257, 258, 260, 264, 272, 288, 320, 368, 448, 513, 514, 516, 520, 528, 544, 576, 640, 736, 896, 1025, 1026, 1028, 1032, 1040
OFFSET
1,1
COMMENTS
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
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 1000 terms from Reinhard Zumkeller)
J. D. Currie, There are ternary circular square-free words of length n for n >= 18, Elect. J. Combinatorics 9 (2002), Note #N10.
James D. Currie, and Jesse T. Johnson, There are level ternary circular square-free words of length n for n != 5,7,9,10,14,17, arXiv:2005.06235 [math.CO], 2020.
Arseny M. Shur, On Ternary Square-free Circular Words, Electronic J. Combin., Volume 17 (2010), Research Paper #R140.
FORMULA
a(n)^2 = A212190(n).
MATHEMATICA
Select[Range[1, 1000], Total[IntegerDigits[#^2, 2]] == 3 &] (* T. D. Noe, Dec 07 2012 *)
PROG
(Haskell)
a212191 n = a212191_list !! (n-1)
a212191_list = map a000196 a212190_list
CROSSREFS
Cf. A000196, A005009 (subsequence).
Sequence in context: A138579 A189703 A158251 * A336122 A241853 A165513
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, May 03 2012
STATUS
approved