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A323424
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Number of cycles (mod n) under Collatz map.
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1
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1, 1, 2, 1, 2, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 4, 2, 2, 2, 3, 2, 2, 2, 3, 2, 3, 3, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 2, 4, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 2, 2, 2, 3, 3, 2, 2, 3, 2, 2, 2, 4, 2, 2, 2, 3
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OFFSET
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1,3
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COMMENTS
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This sequence is likely to be unbounded.
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LINKS
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FORMULA
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a(n) >= 2 for any n > 4 (as we have at least the cycles (0) and (1, 4, 2)).
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EXAMPLE
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The initial terms, alongside the corresponding cycles, are:
n a(n) cycles
-- ---- --------------------
1 1 (0)
2 1 (0)
3 2 (0), (1)
4 1 (0)
5 2 (0), (1, 4, 2)
6 2 (0), (1, 4, 2)
7 3 (0), (1, 4, 2), (3)
8 2 (0), (1, 4, 2)
9 2 (0), (1, 4, 2)
10 2 (0), (1, 4, 2)
11 3 (0), (1, 4, 2), (5)
12 2 (0), (1, 4, 2)
13 3 (0), (1, 4, 2), (3, 10, 5)
14 2 (0), (1, 4, 2)
15 3 (0), (1, 4, 2), (7)
16 2 (0), (1, 4, 2)
17 2 (0), (1, 4, 2)
18 2 (0), (1, 4, 2)
19 3 (0), (1, 4, 2), (9)
20 2 (0), (1, 4, 2)
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PROG
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(PARI) a(n, f = k -> if (k%2, 3*k+1, k/2)) = { my (c=0, s=0); for (k=0, n-1, if (!bittest(s, k), my (v=0, i=k); while (1, v += 2^i; i = f(i) % n; if (bittest(s, i), break, bittest(v, i), c++; break)); s += v)); return (c) }
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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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