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

Author

Reinhard Zumkeller, May 03 2012

Keywords

• nonn

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.

Crossrefs

Cf. A000196, A005009 (subsequence).

Programs

Haskell

a212191 n = a212191_list !! (n-1)
a212191_list = map a000196 a212190_list

Mathematica

Select[Range[1, 1000], Total[IntegerDigits[#^2, 2]] == 3 &] (* T. D. Noe, Dec 07 2012 *)

Formula

a(n)^2 = A212190(n).