

A359527


Nonnegative numbers k such that if 2^i and 2^j appear in the binary expansion of k, then 2^(i OR j) also appears in the binary expansion of k (where OR denotes the bitwise OR operator).


1



0, 1, 2, 3, 4, 5, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 32, 33, 34, 35, 48, 49, 50, 51, 64, 65, 68, 69, 80, 81, 84, 85, 128, 129, 130, 131, 132, 133, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 152, 153, 160, 161, 162, 163, 164, 165, 168, 169, 170, 171
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OFFSET

1,3


COMMENTS

Equivalently, numbers whose binary expansions encode unionclosed finite sets of finite sets of nonnegative integers:
 the encoding is based on a double application of A133457,
 for example: 11 > {0, 1, 3} > {{}, {0}, {0, 1}},
 a unionclosed set f satisfies: for any i and j in f, the union of i and j belongs to f.
For any k >= 0, 2*k belongs to the sequence iff 2*k+1 belongs to the sequence.
This sequence has similarities with A190939; here we consider the bitwise OR operator, there the bitwise XOR operator.
This sequence is infinite as it contains the powers of 2.


LINKS



EXAMPLE

The first terms, alongside the corresponding unionclosed sets, are:
n a(n) Unionclosed set
  
1 0 {}
2 1 {{}}
3 2 {{0}}
4 3 {{}, {0}}
5 4 {{1}}
6 5 {{}, {1}}
7 8 {{0, 1}}
8 9 {{}, {0, 1}}
9 10 {{0}, {0, 1}}
10 11 {{}, {0}, {0, 1}}
11 12 {{1}, {0, 1}}
12 13 {{}, {1}, {0, 1}}
13 14 {{0}, {1}, {0, 1}}
14 15 {{}, {0}, {1}, {0, 1}}
15 16 {{2}}
16 17 {{}, {2}}
17 32 {{0, 2}}


PROG

(PARI) is(n) = { my (b=vector(hammingweight(n))); for (i=1, #b, n = 2^b[i] = valuation(n, 2)); setbinop(bitor, b)==b }


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



