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A364969
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a(n) = a(a(n-1)) if n is even, a(n) is the number of times a(n-1) occurs in the sequence so far if n is odd, with a(1) = 1.
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0
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1, 1, 2, 1, 3, 2, 2, 1, 4, 1, 5, 3, 2, 1, 6, 2, 5, 3, 3, 2, 6, 2, 7, 2, 8, 1, 7, 2, 9, 4, 2, 1, 8, 1, 9, 4, 3, 2, 11, 5, 3, 2, 12, 3, 7, 2, 13, 2, 14, 1, 10, 1, 11, 5, 4, 1, 12, 3, 8, 1, 13, 2, 15, 6, 3, 2, 16, 2, 17, 5, 5, 3, 10, 1, 14, 1, 15, 6, 4, 1, 16, 2
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OFFSET
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1,3
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COMMENTS
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Conjecture: All positive integers appear in the sequence.
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LINKS
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EXAMPLE
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a(1) = 1 (by definition).
a(2) = a(a(1)) = a(1) = 1 (2 is even).
a(3) = number of times a(2) occurs = number of times 1 occurs = 2 (3 is odd).
a(4) = a(a(3)) = a(2) = 1 (4 is even).
a(5) = number of times a(4) occurs = number of times 1 occurs = 3 (5 is odd).
a(6) = a(a(5)) = a(3) = 2 (6 is even).
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PROG
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(PARI) lista(nn) = my(va = vector(nn)); va[1] = 1; for (n=2, nn, if (n%2, va[n] = #select(x->(x==va[n-1]), va), va[n] = va[va[n-1]]); ); va; \\ Michel Marcus, Oct 23 2023
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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