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A127886
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Steps saved by choice in "3x+1" iteration
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3
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0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 88, 8, 0, 0, 75, 0, 8, 0, 0, 8, 8, 0, 8, 0, 88, 0, 8, 0, 0, 0, 75, 0, 8, 8, 0, 0, 0, 88, 88, 8, 8, 0, 8, 0, 0, 75, 75, 0, 8, 8, 0, 0, 0, 0, 75, 8
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,9
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COMMENTS
| Normal "3x+1" iteration requires x->x/2 if x is even. a(n) is the number of iterations that can be saved by also allowing x->3x+1 if x is even.
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FORMULA
| a(n) = A006577(n) - A127885(n)
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EXAMPLE
| a(9) = 8 because for 9 the traditional 3x+1 iteration follows the 19-step path:
9 -> 28 -> 14 -> 7 -> 22 -> 11 -> 34 -> 17 -> 52 -> 26 -> 13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1
while allowing x->3x+1 for even x gives the 11-step path:
9 -> 28 -> 85 -> 256 -> 128 -> 64 -> 32 -> 16 -> 8 -> 4 -> 2 -> 1
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CROSSREFS
| A127887 gives the indices of the nonzero entries.
Sequence in context: A128820 A067485 A180225 * A085121 A079204 A199619
Adjacent sequences: A127883 A127884 A127885 * A127887 A127888 A127889
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KEYWORD
| nonn
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AUTHOR
| David Applegate (david(AT)research.att.com) and N. J. A. Sloane (njas(AT)research.att.com), Feb 04 2007
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