OFFSET

1,1

COMMENTS

a(n) is the index of zeros in the complement of the pentagonal number analog of the Baum-Sweet sequence, which is b(n) = 1 if the binary representation of n contains no block of consecutive zeros of exactly a nontrivial pentagonal number length A000326(i) for i>1; otherwise b(n) = 0.

REFERENCES

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

LINKS

J.-P. Allouche, Finite Automata and Arithmetic, SÃ©minaire Lotharingien de Combinatoire, B30c (1993), 23 pp.

EXAMPLE

a(1) = 32 because 32 (base 2) = 100000, which has a block of 5 = A000326(2) zeros.

a(2) = 65 because 65 (base 2) = 1000001, which has a block of 5 zeros.

64 is not in this sequence because, though 64 (base 2) = 1000000 has a block of 6 zeros, which has subblocks of 5 zeros, subblocks do not count.

2080 is in this sequence because 2080 (base 2) = 100000100000 has 2 blocks of 5 zeros, but we do not require only one such 5-zero block.

4096 is in this sequence because 4096 (base 2) = 1000000000000, which has a block of 12 = A000326(3) zeros, as do 8193 and many more.

4194304 is in this sequence because 4194304 (base 2) = 10000000000000000000000, which has a block of 22 = A000326(4) zeros.

CROSSREFS

KEYWORD

base,easy,nonn

AUTHOR

Jonathan Vos Post, Sep 12 2005

EXTENSIONS

Corrected by Ray Chandler, Sep 17 2005

STATUS

approved