A110562 Numbers n such that n in binary representation has a block of exactly a nontrivial pentagonal number of zeros.

32, 65, 96, 130, 131, 160, 193, 224, 260, 261, 262, 263, 288, 321, 352, 386, 387, 416, 449, 480, 520, 521, 522, 523, 524, 525, 526, 527, 544, 577, 608, 642, 643, 672, 705, 736, 772, 773, 774, 775, 800, 833, 864, 898, 899, 928, 961, 992, 1040, 1041, 1042

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

Table of n, a(n) for n=1..51.

J.-P. Allouche, Finite Automata and Arithmetic, Séminaire 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 sub-blocks of 5 zeros, sub-blocks 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

Cf. A000326, A037011, A086747, A110471, A110472, A110474, A110502, A110529.

Sequence in context: A235057 A339358 A249116 * A275187 A045048 A132773

Adjacent sequences: A110559 A110560 A110561 * A110563 A110564 A110565

Keyword

base,easy,nonn

Author

Jonathan Vos Post, Sep 12 2005

Extensions

Corrected by Ray Chandler, Sep 17 2005

Status

approved