A357753 a(n) is the least square with n binary digits.
4, 9, 16, 36, 64, 144, 256, 529, 1024, 2116, 4096, 8281, 16384, 33124, 65536, 131769, 262144, 525625, 1048576, 2099601, 4194304, 8392609, 16777216, 33558849, 67108864, 134235396, 268435456, 536895241, 1073741824, 2147488281, 4294967296, 8589953124, 17179869184
Offset: 3
Programs
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Maple
a:= n-> ceil(sqrt(2)^(n-1))^2: seq(a(n), n=3..35); # Alois P. Heinz, Oct 13 2022
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Mathematica
Array[Ceiling[Sqrt[2^(# - 1)]]^2 &, 33, 3]
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PARI
for (n=3, 35, for(k=0, oo, if(#digits(k^2,2)==n, print1(k^2,", "); break)))
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PARI
a(n) = if(n%2 == 1, 1 << (n-1), ceil(sqrt(1<<(n-1)))^2) \\ David A. Corneth, Oct 11 2022
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Python
from math import isqrt def A357753(n): return 1<
Chai Wah Wu, Oct 13 2022
Formula
a(n) = A017912(n-1)^2.
a(2n+1) = (2^n)^2 = 4^n, for n>=1; indeed: 4^n_{10} = 10^(2n){2} that is the least number with 2n+1 binary digits. - _Bernard Schott, Oct 15 2022