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A346369
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a(n) is the number of steps the Collatz trajectory of -n takes to reach a cycle, or -1 if no cycle is ever reached.
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0
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0, 0, 3, 1, 0, 4, 0, 2, 7, 0, 5, 5, 5, 0, 8, 3, 0, 8, 3, 0, 6, 6, 1, 6, 0, 6, 3, 1, 9, 9, 4, 4, 11, 0, 9, 9, 0, 4, 12, 1, 0, 7, 7, 7, 5, 2, 12, 7, 9, 0, 7, 7, 15, 4, 0, 2, 28, 10, 10, 10, 0, 5, 15, 5, 36, 12, 3, 0, 18, 10, 18, 10, 7, 0, 5, 5, 13, 13, 13, 2, 18
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OFFSET
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1,3
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COMMENTS
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The analog of A139399 for negative starting values.
Is a(n) > -1 for all n?
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LINKS
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FORMULA
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EXAMPLE
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For n = 5: The trajectory of -5 starts -5, -14, -7, -20, -10, -5, -14, -7, -20, -10, -5, ..., with -5 already being part of the cycle {-5, -14, -7, -20, -10}, so a(5) = 0.
For n = 6: The trajectory of -6 starts -6, -3, -8, -4, -2, -1, -2, -1, -2, -1, -2, ..., reaching a term of the cycle {-2, -1} after 4 steps, so a(6) = 4.
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PROG
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(PARI) a006370(n) = if(n%2==0, n/2, 3*n+1)
trajectory(n, terms) = my(v=[n]); while(#v < terms, v=concat(v, a006370(v[#v]))); v
a(n) = my(t, v=[]); for(k=1, oo, t=trajectory(-n, k); for(x=1, #t, if(x < #t && t[x]==t[#t], return(x-1))))
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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