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%I #31 Feb 07 2018 18:16:22
%S 0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,
%T 0,0,1,1,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,
%U 0,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0
%N Second most significant bit of Fibonacci numbers > 1 written in base 2.
%C It is conjectured that there are no more than two consecutive "0's" or “1’s” (tested up to n=10^5). The sequence looks quasiperiodic and its Fourier spectrum seems to have a fractal structure.
%H Chai Wah Wu, <a href="/A272170/b272170.txt">Table of n, a(n) for n = 3..10000</a>
%F a(n) = floor(A000045(n)/(2^(ceiling(log_2(A000045(n) + 1)) - 2))) - 2.
%F a(n) = A079944(A000045(n)-2). - _Michel Marcus_, Apr 22 2016
%e (second MSB in parenthesis)
%e n A000045(n) A004685(n)
%e 3 2 -> 1(0)
%e 4 3 -> 1(1)
%e 5 5 -> 1(0)1
%e 6 8 -> 1(0)00
%e 7 13 -> 1(1)01
%e 8 21 -> 1(0)101
%e 9 34 -> 1(0)0010
%e 10 55 -> 1(1)0111
%e ...
%t nmax = 120; Table[IntegerDigits[Fibonacci[j], 2][[2]], {j, 3, nmax}]
%o (PARI) a(n) = binary(fibonacci(n))[2]; \\ _Michel Marcus_, Apr 25 2016
%o (Python)
%o A272170_list, a, b = [], 1 ,1
%o for n in range(3,10001):
%o a, b = b, a+b
%o A272170_list.append(int(bin(b)[3])) # _Chai Wah Wu_, Feb 07 2018
%Y Cf. A000045, A004685, A079944, A271591.
%K nonn,base
%O 3,1
%A _Andres Cicuttin_, Apr 21 2016
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