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

%I A357754 #25 Oct 13 2022 15:27:58
%S A357754 4,9,25,49,121,225,484,961,2025,3969,8100,16129,32761,65025,131044,
%T A357754 261121,524176,1046529,2096704,4190209,8386816,16769025,33547264,
%U A357754 67092481,134212225,268402689,536848900,1073676289,2147395600,4294836225,8589767761,17179607041,34359441769
%N A357754 a(n) is the largest square with n binary digits.
%F A357754 a(n) = 2^n - A056007(n). - _Kevin Ryde_, Oct 13 2022
%F A357754 a(n) = A116601(n+2)^2. - _Michel Marcus_, Oct 13 2022
%t A357754 Array[Floor[Sqrt[2^# - 1]]^2 &, 33, 3] (* _Michael De Vlieger_, Oct 11 2022 *)
%o A357754 (PARI) for (n=3, 35, forstep (k2=2^n-1, 2^(n-1), -1, if (issquare(k2), print1(k2,", "); break)))
%o A357754 (PARI) a(n) = if(n%2 == 1, (sqrt(1<<n)\1)^2, ((1 << (n\2)) - 1)^2) \\ _David A. Corneth_, Oct 11 2022
%o A357754 (Python)
%o A357754 from math import isqrt
%o A357754 def A357754(n): return (isqrt((1<<n)-1) if n&1 else (1<<(n>>1))-1)**2 # _Chai Wah Wu_, Oct 13 2022
%Y A357754 Cf. A000290, A070939, A056007, A116601, A357753.
%K A357754 nonn,base,easy
%O A357754 3,1
%A A357754 _Hugo Pfoertner_, Oct 11 2022