A110471 Prime analog of Baum-Sweet sequence: a(n) = 1 if binary representation of n contains no block of consecutive zeros of exactly prime length; otherwise a(n) = 0.

1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Author

Jonathan Vos Post, Sep 07 2005

Keywords

• base
• easy
• nonn

Examples

			a(4) = 0 because 4 (base 2) = 100, which has 2 (prime) consecutive zeros.
a(8) = 0 because 8 (base 2) = 1000, which has 3 (prime) consecutive zeros.
a(9) = 0 because 9 (base 2) = 1001, which has 2 (prime) consecutive zeros.
a(16) = 1 because 16 (base 2) = 10000, which has 4 (composite) consecutive zeros, even though there are subblocks of zeros of lengths 2 and 3.
a(32) = 0 because 32 (base 2) = 100000, which has 5 (prime) consecutive zeros.
		

References

• J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 157.

Links

• J.-P. Allouche, Finite Automata and Arithmetic, Séminaire Lotharingien de Combinatoire, B30c (1993), 23 pp.

Crossrefs

Cf. A037011, A086747, A110472, A110474.

Programs

Mathematica

f[n_] := If[Or @@ (First[ # ] == 0 && PrimeQ[Length[ # ]] &) /@ Split[IntegerDigits[n, 2]], 0, 1]; Table[f[n], {n, 0, 120}] (* Ray Chandler, Sep 16 2005 *)

Extensions

Extended by Ray Chandler, Sep 16 2005