

A357304


Records of the Hamming weight of squares.


5



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
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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 90bit 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



