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A271591 Second most significant bit of the tribonacci number A000073(n). 4

%I

%S 0,0,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0,0,

%T 1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0,0,1,

%U 1,1,1,0,0,0,0,0,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0,1,1

%N Second most significant bit of the tribonacci number A000073(n).

%C It is conjectured that after the first two 0's, the number of consecutive 0's is only 4 or 5, and the number of consecutive 1's is only 3 or 4 (tested up to n=10^4). The sequence looks quasiperiodic (or with a very long true period if any).

%H Chai Wah Wu, <a href="/A271591/b271591.txt">Table of n, a(n) for n = 4..10000</a>

%F a(n) = floor(A000073(n)/(2^(ceiling(log_2(A000073(n) + 1)) - 2))) - 2.

%F a(n) = A079944(A000073(n)-2). - _Michel Marcus_, Apr 22 2016

%e (Second MSB in parenthesis)

%e n A000073(n) A000073(n)

%e decimal binary

%e 4 2 -> 1(0)

%e 5 4 -> 1(0)0

%e 6 7 -> 1(1)1

%e 7 13 -> 1(1)01

%e 8 24 -> 1(1)000

%e 9 44 -> 1(0)1100

%e 10 81 -> 1(0)10001

%e 11 149 -> 1(0)010101

%t a = LinearRecurrence[{1, 1, 1}, {0, 0, 1}, 120];(* to generate A000073 *)

%t Table[IntegerDigits[a, 2][[i]][[2]], {i, 5, Length[a]}]

%o (Python)

%o A271591_list, a, b, c = [], 0, 1 ,1

%o for n in range(4,10001):

%o a, b, c = b, c, a+b+c

%o A271591_list.append(int(bin(c)[3])) # _Chai Wah Wu_, Feb 07 2018

%Y Cf. A000073 (tribonacci numbers), A079944 (2nd msb), A272170.

%K nonn,base

%O 4,1

%A _Andres Cicuttin_, Apr 10 2016

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Last modified December 7 20:30 EST 2019. Contains 329849 sequences. (Running on oeis4.)