A323062 - OEIS

A323062

Numbers m > 0 such that floor(sqrt(2^(2m-1))) > 1/2 + sqrt(1/4 + 2^(2m-1) - 2^m).

%I #14 Jan 11 2019 16:02:40

%S 8,9,10,11,20,24,47,51,54,57,58,59,62,63,69,81,82,106,128,147,148,149,

%T 150,161,162,165,181,182,183,186,200,201,214,217,218,219,225,226,227,

%U 228,232,241,245,248,249,258,270,273,274,275,276,280,281,282,283,286

%N Numbers m > 0 such that floor(sqrt(2^(2m-1))) > 1/2 + sqrt(1/4 + 2^(2m-1) - 2^m).

%C m is a term if and only if floor(sqrt(2^(2m-1))) is a term of A323192. Equivalently, a(n) is the number of bits of the binary representation of A323192(n).

%H Chai Wah Wu, <a href="/A323062/b323062.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A070939(A323192(n)) = (A070939(A323192(n)^2)+1)/2.

%F A323192(n) = A000196(2^(2*a(n)-1)).

%o (Python)

%o from sympy import integer_nthroot

%o A323062_list = [k for k in range(1,10000) if (2*integer_nthroot(2**(2*k-1),2)[0]-1)**2 > 1 + 4*(2**(2*k-1) - 2**k)] # _Chai Wah Wu_, Jan 11 2019

%Y Cf. A000196, A070939, A323192.

%K nonn

%O 1,1

%A _Chai Wah Wu_, Jan 10 2019