A357304 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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.