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A352199
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a(0)=0, a(1)=1, a(2)=2; thereafter, a(n) is smallest number m not yet in the sequence such that the binary expansions of m and a(n-2) have a 1 in common, but the 1's in m are disjoint from the 1's in a(n-1) and a(n-3).
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1
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0, 1, 2, 5, 10, 4, 8, 20, 9, 6, 33, 18, 32, 14, 96, 3, 48, 7, 16, 11, 80, 12, 64, 13, 66, 17, 34, 21, 40, 65, 42, 68, 24, 69, 26, 36, 130, 37, 74, 49, 72, 52, 136, 19, 128, 22, 160, 15, 192, 23, 224, 25, 288, 27, 100, 129, 260, 131, 28, 35, 76, 161, 84, 162, 88
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OFFSET
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0,3
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COMMENTS
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An equivalent definition in terms of sets: S(0) = {}, S(1) = {1}, S(2} = {1,2}; thereafter S(n) is the smallest set (different from the S{i} already defined) of positive integers such that S(n) meets S(n-2) but is disjoint from S(n-1) and S(n-3}.
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LINKS
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EXAMPLE
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After a(4) = 10 = 1010_2, a(5) = 4 = 100_2, a(6) = 8 = 1000_2, a(7) must have the form ...?010?_2, and the smallest missing number of that form is 20 = 10100_2 = 20.
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PROG
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(PARI) { s=0; for (n=1, #a=vector(65), if (n<=3, a[n]=n-1, for (v=0, oo, if (!bittest(s, v) && bitand(v, a[n-2]) && !bitand(v, bitor(a[n-3], a[n-1])), a[n]=v; break))); s+=2^a[n]; print1(a[n]", ")) } \\ Rémy Sigrist, Mar 27 2022
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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