A357659 a(n) is the least k such that k^2 has a maximal Hamming weight A357658(n) in the range 2^n <= k^2 < 2^(n+1).

2, 3, 5, 7, 11, 13, 21, 27, 45, 53, 75, 101, 181, 217, 362, 437, 627, 923, 1241, 1619, 2505, 3915, 5221, 6475, 11309, 15595, 19637, 31595, 44491, 61029, 69451, 113447, 185269, 244661, 357081, 453677, 642119, 980853, 1380917, 1961706, 2965685, 3923411, 5931189, 8096813

Offset

2,1

Links

Hugo Pfoertner, Table of n, a(n) for n = 2..125, including results from Bert Dobbelaere and from users l4m2, gsitcia, and anttiP in Code Golf challenge (terms 103..125)

Code Golf Stackexchange, Smallest and largest 100-bit square with maximum Hamming weight, fastest code challenge started Dec 15 2022.

Example

See A357658.

Prog

(Python 3.10+)
from math import isqrt
def A357659(n):
    c = 0
    for k in range(isqrt((1<<n)-1)+1, isqrt((1<<n+1)-1)+1):
        if (d:=(k**2).bit_count()) > c:
            c, m = d, k
        elif d == c:
            m = min(m, k)
    return m # Chai Wah Wu, Oct 14 2022
(C, x64asm, Rust, c++) see Code Golf link.

Crossrefs

Cf. A000120, A000290, A357658, A357660.

Sequence in context: A354800 A280937 A296236 * A334041 A181172 A075430

Adjacent sequences: A357656 A357657 A357658 * A357660 A357661 A357662

Keyword

nonn,base

Author

Hugo Pfoertner, Oct 09 2022

Status

approved