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1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,9
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COMMENTS
| Let f be defined as in A159885. Then a(n) is the least k such that either f^k(2n+1))<2n+1 or A000120(f^k(2n+1)) < A000120(2n+1) or A006694((f^k(2n+1)-1)/2) < A006694(n).
In connection with A160198, A160267, A160322 we pose a new (3x+1)-problem: does there exist a finite number of sequences A_i(n), i=1,...,T, such that: 1) A_i(0)=0 and A_i(n)>0 for n>=1; 2) if B_i(n) denotes the least k for which A_i(n)>A_i((f^k(2n+1)-1)/2), then B(n)=min_{i=1,...,T}B_i(n)=1 for every n>=1? Note that this problem is weaker than (3x+1)-Collatz problem. Indeed, if the Collatz conjecture is true, then there exist nonnegative sequences A(n) for which A(0)=0 and A(n)>A((f(2n+1)-1)/2) for every n>=1 (see A160348). [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), May 15 2009]
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CROSSREFS
| A000120 A006694 A160198 A160267 A122458 A160266 A159885 A159945
Sequence in context: A054977 A078315 A156264 * A087102 A194309 A113515
Adjacent sequences: A160319 A160320 A160321 * A160323 A160324 A160325
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KEYWORD
| nonn,uned
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AUTHOR
| Vladimir Shevelev (shevelev(AT)bgu.ac.il), May 08 2009, May 11 2009
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