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

1,2

Links

Table of n, a(n) for n=1..50.

Formula

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

Example

   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  -  -  -  -  -

Prog

(Python 3.10+)
def A357742(n): return max((k**2).bit_count() for k in range(1<<n-1, 1<<n)) # Chai Wah Wu, Oct 17 2022

Crossrefs

Cf. A000290, A159918, A357304, A357658.

Sequence in context: A030709 A226806 A058588 * A035399 A354852 A153775

Adjacent sequences: A357739 A357740 A357741 * A357743 A357744 A357745

Keyword

nonn,base,hard,more

Author

Karl-Heinz Hofmann and Hugo Pfoertner , Oct 11 2022

Extensions

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

Status

approved