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

3,1

Links

Table of n, a(n) for n=3..35.

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

Maple

a:= n-> ceil(sqrt(2)^(n-1))^2:
seq(a(n), n=3..35);  # Alois P. Heinz, Oct 13 2022

Mathematica

Array[Ceiling[Sqrt[2^(# - 1)]]^2 &, 33, 3]

Prog

(PARI) for (n=3, 35, for(k=0, oo, if(#digits(k^2, 2)==n, print1(k^2, ", "); break)))
(PARI) a(n) = if(n%2 == 1, 1 << (n-1), ceil(sqrt(1<<(n-1)))^2) \\ David A. Corneth, Oct 11 2022
(Python)
from math import isqrt
def A357753(n): return 1<<n-1 if n&1 else (isqrt(1<<n-1)+1)**2 # Chai Wah Wu, Oct 13 2022

Crossrefs

Cf. A000290, A000302, A065732, A070939, A017912, A357754.

Sequence in context: A025620 A117218 A226076 * A272711 A356880 A018228

Adjacent sequences: A357750 A357751 A357752 * A357754 A357755 A357756

Keyword

nonn,base

Author

Hugo Pfoertner, Oct 11 2022

Status

approved