cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A272170 Second most significant bit of Fibonacci numbers > 1 written in base 2.

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%I A272170 #31 Feb 07 2018 18:16:22
%S A272170 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 A272170 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 A272170 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 A272170 Second most significant bit of Fibonacci numbers > 1 written in base 2.
%C A272170 It is conjectured that there are no more than two consecutive "0's" or ā€œ1’sā€ (tested up to n=10^5). The sequence looks quasiperiodic and its Fourier spectrum seems to have a fractal structure.
%H A272170 Chai Wah Wu, <a href="/A272170/b272170.txt">Table of n, a(n) for n = 3..10000</a>
%F A272170 a(n) = floor(A000045(n)/(2^(ceiling(log_2(A000045(n) + 1)) - 2))) - 2.
%F A272170 a(n) = A079944(A000045(n)-2). - _Michel Marcus_, Apr 22 2016
%e A272170 (second MSB in parenthesis)
%e A272170   n   A000045(n)      A004685(n)
%e A272170   3      2       ->   1(0)
%e A272170   4      3       ->   1(1)
%e A272170   5      5       ->   1(0)1
%e A272170   6      8       ->   1(0)00
%e A272170   7      13      ->   1(1)01
%e A272170   8      21      ->   1(0)101
%e A272170   9      34      ->   1(0)0010
%e A272170   10     55      ->   1(1)0111
%e A272170 ...
%t A272170 nmax = 120; Table[IntegerDigits[Fibonacci[j], 2][[2]], {j, 3, nmax}]
%o A272170 (PARI) a(n) = binary(fibonacci(n))[2]; \\ _Michel Marcus_, Apr 25 2016
%o A272170 (Python)
%o A272170 A272170_list, a, b = [], 1 ,1
%o A272170 for n in range(3,10001):
%o A272170     a, b = b, a+b
%o A272170     A272170_list.append(int(bin(b)[3])) # _Chai Wah Wu_, Feb 07 2018
%Y A272170 Cf. A000045, A004685, A079944, A271591.
%K A272170 nonn,base
%O A272170 3,1
%A A272170 _Andres Cicuttin_, Apr 21 2016