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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Equivalently, numbers whose binary expansions encode union-closed 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 union-closed 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 Table of n, a(n) for n=1..60. Wikipedia, Union-closed sets conjecture Index entries for sequences related to binary expansion of n EXAMPLE The first terms, alongside the corresponding union-closed sets, are: n a(n) Union-closed 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 Cf. A133457, A190939 (XOR analog), A359528 (AND analog). Sequence in context: A297163 A319024 A039260 * A039200 A039150 A008539 Adjacent sequences: A359524 A359525 A359526 * A359528 A359529 A359530 KEYWORD nonn,base AUTHOR Rémy Sigrist, Jan 04 2023 STATUS approved

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Last modified September 8 06:50 EDT 2024. Contains 375751 sequences. (Running on oeis4.)