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A176866
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The number of odd numbers that require n Collatz (3x+1) iterations to reach 1.
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9
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1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2, 4, 4, 6, 5, 7, 8, 14, 14, 19, 22, 30, 36, 48, 60, 79, 94, 118, 154, 194, 248, 315, 390, 486, 623, 792, 1008, 1261, 1579, 2007, 2555, 3219, 4043, 5109, 6464, 8204, 10351, 13100, 16575, 20889, 26398, 33388, 42155, 53370, 67414
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OFFSET
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0,8
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COMMENTS
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Both the 3x+1 steps and the halving steps are counted. The asymptotic growth rate appears to be the same as A005186, about 1.26 (A176014).
a(n) is, for n >= 4, the number of 4 (mod 6) nodes (vertices) of row n-1 of the Collatz tree A127824. The node 4 has in A127824 outdegree 1 in order to avoid a repetition of the whole tree. - Wolfdieter Lang, Mar 26 2014
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LINKS
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EXAMPLE
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23, 141, 151, 853, 909, and 5461 are the only odd numbers that require exactly 15 iterations to reach 1. Hence a(15)=6.
At row 15 with a(16) = 5 nodes 4 (mod 6) the left-right symmetry for the number of 4 (mod 6) nodes in the Collatz tree A127824 is broken for the first time: in the left half of the tree there are the three nodes 22, 136 and 832 but on the right half only the two nodes 904 and 5440. - Wolfdieter Lang, Mar 26 2014
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CROSSREFS
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Cf. A005186 (number of numbers having stopping time n).
Cf. A127824 (numbers having stopping time n).
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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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