1,9

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]

A000120 A006694 A160198 A160267 A122458 A160266 A159885 A159945

Sequence in context: A054977 A078315 A156264 this_sequence A087102 A113515 A103754

Adjacent sequences: A160319 A160320 A160321 this_sequence A160323 A160324 A160325

nonn,uned

Vladimir Shevelev (shevelev(AT)bgu.ac.il), May 08 2009, May 11 2009