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

3,1

Links

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

Formula

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

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

Mathematica

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

Prog

(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<<n)\1)^2, ((1 << (n\2)) - 1)^2) \\ David A. Corneth, Oct 11 2022
(Python)
from math import isqrt
def A357754(n): return (isqrt((1<<n)-1) if n&1 else (1<<(n>>1))-1)**2 # Chai Wah Wu, Oct 13 2022

Crossrefs

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

Sequence in context: A158183 A158184 A001255 * A133019 A326708 A028866

Adjacent sequences: A357751 A357752 A357753 * A357755 A357756 A357757

Keyword

nonn,base,easy

Author

Hugo Pfoertner, Oct 11 2022

Status

approved