This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A357304 #21 Nov 30 2022 10:59:12
%S A357304 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,
%T A357304 29,30,31,33,34,35,37,38,39,40,41,42,44,45,46,47,48,49,50,51,52,53,54,
%U A357304 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
%N A357304 Records of the Hamming weight of squares.
%e A357304 a(70) = 77 corresponds to A230097(70) = 34895284158283. Its square 1217680856487316499797508089 is the smallest and the only 90-bit square with this Hamming weight.
%o A357304 (Python 3.10+)
%o A357304 from itertools import count, islice
%o A357304 def A357304_gen(): # generator of terms
%o A357304 c = -1
%o A357304 for n in count(0):
%o A357304 if (m := (n**2).bit_count() if sys.version_info >= (3,10) else bin(n**2).count('1'))>c:
%o A357304 yield (c:=m)
%o A357304 A357304_list = list(islice(A357304_gen(),20)) # _Chai Wah Wu_, Oct 01 2022
%Y A357304 A230097 gives the values of k such that A000120(k^2) sets a new record.
%Y A357304 Cf. A000120, A000290, A159918, A357658.
%K A357304 nonn,hard
%O A357304 1,3
%A A357304 _Hugo Pfoertner_, Oct 01 2022
%E A357304 Missing a(68)=75 and a(71)-a(80) from _Bert Dobbelaere_, Nov 20 2022