A212191 Numbers whose squares are the sum of exactly three distinct powers of 2.

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

Adjacent sequences: A212188 A212189 A212190 * A212192 A212193 A212194

Keyword

nonn

Author

Reinhard Zumkeller, May 03 2012

Status

approved