A323192 -id:A323192

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A323062

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

+0
1

8, 9, 10, 11, 20, 24, 47, 51, 54, 57, 58, 59, 62, 63, 69, 81, 82, 106, 128, 147, 148, 149, 150, 161, 162, 165, 181, 182, 183, 186, 200, 201, 214, 217, 218, 219, 225, 226, 227, 228, 232, 241, 245, 248, 249, 258, 270, 273, 274, 275, 276, 280, 281, 282, 283, 286

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OFFSET

1,1

COMMENTS

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).

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10000

FORMULA

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

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

PROG

(Python)

from sympy import integer_nthroot

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

CROSSREFS

Cf. A000196, A070939, A323192.

KEYWORD

nonn

AUTHOR

Chai Wah Wu, Jan 10 2019

STATUS

approved

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