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A357304
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Records of the Hamming weight of squares.
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5
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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)
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OFFSET
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1,3
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LINKS
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Table of n, a(n) for n=1..80.
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EXAMPLE
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a(70) = 77 corresponds to A230097(70) = 34895284158283. Its square 1217680856487316499797508089 is the smallest and the only 90-bit square with this Hamming weight.
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PROG
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(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
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CROSSREFS
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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
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KEYWORD
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nonn,hard
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AUTHOR
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Hugo Pfoertner, Oct 01 2022
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EXTENSIONS
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Missing a(68)=75 and a(71)-a(80) from Bert Dobbelaere, Nov 20 2022
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STATUS
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approved
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