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A335870
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a(n) is the least k > 0 such that T^k(n) = T^(2*k)(n) (where T^k denotes the k-th iterate of A006370, the Collatz map); a(n) = -1 if no such k exists.
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1
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1, 3, 3, 6, 3, 3, 6, 15, 3, 18, 6, 12, 9, 9, 15, 15, 3, 12, 18, 18, 6, 6, 15, 15, 9, 21, 9, 111, 18, 18, 18, 105, 3, 24, 12, 12, 21, 21, 21, 33, 6, 108, 6, 27, 15, 15, 15, 102, 9, 24, 24, 24, 9, 9, 111, 111, 18, 30, 18, 30, 18, 18, 105, 105, 6, 27, 27, 27, 12
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OFFSET
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0,2
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COMMENTS
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If the Collatz conjecture is true, then a(n) > 0 for all n >= 0.
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LINKS
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EXAMPLE
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For n = 3 we have:
k T^k(3) T^(2*k)(3)
- ------ ----------
1 10 5
2 5 8
3 16 2
4 8 4
5 4 1
6 2 2
so a(3) = 6.
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PROG
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(PARI) a(n, T=x->if (x%2, 3*x+1, x/2)) = my (x1=n, x2=n); for (k=1, oo, x1=T(x1); x2=T(T(x2)); if (x1==x2, return (k)))
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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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