A357304 Records of the Hamming weight of squares.

0, 1, 2, 3, 5, 6, 7, 8, 9, 10, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 85, 87, 88, 89

Offset

1,3

Links

Table of n, a(n) for n=1..80.

Example

a(70) = 77 corresponds to A230097(70) = 34895284158283. Its square 1217680856487316499797508089 is the smallest and the only 90-bit square with this Hamming weight.

Prog

(Python 3.10+)
from itertools import count, islice
def A357304_gen(): # generator of terms
    c = -1
    for n in count(0):
        if (m := (n**2).bit_count() if sys.version_info >= (3, 10) else bin(n**2).count('1'))>c:
            yield (c:=m)
A357304_list = list(islice(A357304_gen(), 20)) # Chai Wah Wu, Oct 01 2022

Crossrefs

A230097 gives the values of k such that A000120(k^2) sets a new record.

Cf. A000120, A000290, A159918, A357658.

Sequence in context: A003251 A288315 A285980 * A268231 A039167 A247360

Adjacent sequences: A357301 A357302 A357303 * A357305 A357306 A357307

Keyword

nonn,hard

Author

Hugo Pfoertner, Oct 01 2022

Extensions

Missing a(68)=75 and a(71)-a(80) from Bert Dobbelaere, Nov 20 2022

Status

approved