A394988 a(n) is the maximum Hamming weight of the product x*y of two integers 2^(n-1) <= x <= y < 2^n.

1, 2, 4, 6, 8, 10, 12, 15, 17, 18, 20, 22, 25, 26, 28, 30, 32, 35, 36, 39, 40, 43, 45, 47, 48, 50, 52, 55, 56, 58, 60, 63, 65, 66, 68, 70, 72, 75, 76, 78, 81, 82, 85, 87, 88, 90, 93, 95, 96, 99, 100, 102, 105, 106, 108, 111, 113, 115, 117, 119, 120, 122, 125

Offset

1,2

Links

Chai Wah Wu, Table of n, a(n) for n = 1..95

Example

See A384987 and A394991.

Prog

(Python)
from sympy.utilities.iterables import multiset_permutations
from sympy import divisors
def A394988(n):
    a = 1<<n-1
    b = a<<1
    k = (n<<1)-1
    for l in range(k, 0, -1):
        for s in multiset_permutations('0'*(k+1-l)+'1'*l):
            m = int(''.join(s), 2)
            for d in divisors(m):
                if d**2>m:
                    break
                if a<=d<b and a*d<=m<b*d:
                    return l # Chai Wah Wu, Apr 09 2026

Crossrefs

Cf. A000120, A053644, A394987, A394991.

Sequence in context: A255385 A187412 A187473 * A287122 A064997 A292651

Adjacent sequences: A394985 A394986 A394987 * A394989 A394990 A394991

Keyword

nonn

Author

Hugo Pfoertner, Apr 09 2026

Extensions

a(24)-a(63) from Chai Wah Wu, Apr 09 2026

Status

approved