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A186447
a(n)=a(floor(n/3)+a(n-1)*floor(n/4)) XOR a(floor(n/2))
0
1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1
OFFSET
0
COMMENTS
A simple unpredictable binary sequence.
Conjecture: All finite binary words appear in the sequence infinitely many times.
The sequence appears to have a slight bias towards 0. From n=0 through n=999, there are 510 1's. But after 10000 terms, the sequence has produced only 4900 1's. And after 10000000 terms, the sequence has produced 4910267 1's.
EXAMPLE
For n=20, a(n)=a(10) XOR a(floor(20/3)+a(19)*5)
=0 XOR a(11)=0 XOR 0 =0.
MATHEMATICA
f[0] = f[1] = 1; f[n_] := f[n] =
Mod[f[Floor[n/3] + f[n - 1] Floor[n/4]] + f[Floor[n/2]], 2]; Table[f[n], {n, 0, 100}]
CROSSREFS
Sequence in context: A374036 A087049 A358680 * A118009 A113429 A133100
KEYWORD
nonn
AUTHOR
Ben Branman, Feb 21 2011
STATUS
approved