A357742 a(n) is the maximum binary weight of the squares of n-bit numbers.

1, 2, 3, 5, 6, 8, 9, 13, 13, 15, 16, 18, 20, 22, 24, 25, 27, 29, 31, 34, 34, 37, 38, 39, 41, 44, 44, 47, 49, 51, 52, 54, 55, 57, 59, 63, 63, 64, 66, 68, 69, 72, 73, 76, 77, 78, 80, 82, 85, 87

Offset: 1

Author

Karl-Heinz Hofmann and Hugo Pfoertner , Oct 11 2022

Keywords

• nonn
• base
• hard
• more

Examples

			   bit   |
  length |          possible binary weight of k^2
   of k  | 0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20
   = n   |          the rightmost value is a(n)
  -------+--------------------------------------------------------------
     1   | 0  1
     2   |    1  2  -  -
     3   |    1  2  3  -  -  -
     4   |    1  2  3  4  5  -  -  -
     5   |    1  2  3  4  5  6  -  -  -  -
     6   |    1  2  3  4  5  6  7  8  -  -  -  -
     7   |    1  2  3  4  5  6  7  8  9  -  -  -  -  -
     8   |    1  2  3  4  5  6  7  8  9 10 11  - 13  -  -  -
     9   |    1  2  3  4  5  6  7  8  9 10 11 12 13  -  -  -  -  -
    10   |    1  2  3  4  5  6  7  8  9 10 11 12 13 14 15  -  -  -  -  -
		

Crossrefs

Cf. A000290, A159918, A357304, A357658.

Formula

a(n) = max(A357658(2*n-2), A357658(2*n-1)).

Extensions

a(47)-a(50) from Martin Ehrenstein, Dec 26 2023