A357754 a(n) is the largest square with n binary digits.

4, 9, 25, 49, 121, 225, 484, 961, 2025, 3969, 8100, 16129, 32761, 65025, 131044, 261121, 524176, 1046529, 2096704, 4190209, 8386816, 16769025, 33547264, 67092481, 134212225, 268402689, 536848900, 1073676289, 2147395600, 4294836225, 8589767761, 17179607041, 34359441769

Offset: 3

Author

Hugo Pfoertner, Oct 11 2022

Keywords

• nonn
• base
• easy

Crossrefs

Cf. A000290, A070939, A056007, A116601, A357753.

Programs

Mathematica

Array[Floor[Sqrt[2^# - 1]]^2 &, 33, 3] (* Michael De Vlieger, Oct 11 2022 *)

PARI

for (n=3, 35, forstep (k2=2^n-1, 2^(n-1), -1, if (issquare(k2), print1(k2,", "); break)))

PARI

a(n) = if(n%2 == 1, (sqrt(1<David A. Corneth, Oct 11 2022

Python

from math import isqrt
def A357754(n): return (isqrt((1<>1))-1)**2 # Chai Wah Wu, Oct 13 2022

Formula

a(n) = 2^n - A056007(n). - Kevin Ryde, Oct 13 2022

a(n) = A116601(n+2)^2. - Michel Marcus, Oct 13 2022