A186447 a(n)=a(floor(n/3)+a(n-1)*floor(n/4)) XOR a(floor(n/2))

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.

Links

Table of n, a(n) for n=0..100.

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: A095901 A087049 A358680 * A118009 A113429 A133100

Adjacent sequences: A186444 A186445 A186446 * A186448 A186449 A186450

Keyword

nonn

Author

Ben Branman, Feb 21 2011

Status

approved