

A110562


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


0



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
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OFFSET

1,1


COMMENTS

a(n) is the index of zeros in the complement of the pentagonal number analog of the BaumSweet 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, 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 5zero 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: A256819 A235057 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



