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A271591
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Second most significant bit of the tribonacci number A000073(n).
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4
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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, 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, 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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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4,1
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COMMENTS
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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).
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LINKS
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FORMULA
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a(n) = floor(A000073(n)/(2^(ceiling(log_2(A000073(n) + 1)) - 2))) - 2.
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EXAMPLE
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(Second MSB in parenthesis)
decimal binary
4 2 -> 1(0)
5 4 -> 1(0)0
6 7 -> 1(1)1
7 13 -> 1(1)01
8 24 -> 1(1)000
9 44 -> 1(0)1100
10 81 -> 1(0)10001
11 149 -> 1(0)010101
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MATHEMATICA
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a = LinearRecurrence[{1, 1, 1}, {0, 0, 1}, 120]; (* to generate A000073 *)
Table[IntegerDigits[a, 2][[i]][[2]], {i, 5, Length[a]}]
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PROG
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(Python)
A271591_list, a, b, c = [], 0, 1 , 1
for n in range(4, 10001):
a, b, c = b, c, a+b+c
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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