Search: id:A098860
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%I A098860
%S A098860 3,5,7,29,41,79,89,107,109,127,149,157,179,191,199,211
%N A098860 Primes that are conjectured to lead to a one-cycle for every natural 
               number x in the following (nontrivial) generalization of the (3x+1) 
               problem.
%C A098860 Start with a number x and construct a successor by the following iterative 
               procedure: first remove all factors 2, 3, 5, ..., p(k) from x, where 
               p(k) is the k-th prime number. When no further such factors remain 
               then take the number ([p(k+1)*x]+1)/2 as the successor. The (3x+1) 
               problem is the special case k=1 in the sequence that lists the p(k+1) 
               leading to a one-cycle.
%C A098860 For other primes there is at least 1 supplementary cycle: e.g. when p(k+1)=11 
               there is also a cycle starting with 17; when p(k+1)=19 there is also 
               a cycle starting with 46063; when p(k+1)=61 there are 3 supplementary 
               cycles starting resp. with 97, 199, 26833; etc.
%t A098860 v[n_, k_]:=Block[{m=n}, Do[While[Mod[m, Prime[i]]==0, m=m/Prime[i]], 
               {i, k}]; If[m!=1, Prepend[v[m*Prime[k+1]+1, k], m], v[m, k]={1}]] 
               b[r_, s_, t_]:=Table[v[n, r], {n, s, t}]
%Y A098860 Sequence in context: A046931 A154551 A058047 this_sequence A106920 A060273 
               A124077
%Y A098860 Adjacent sequences: A098857 A098858 A098859 this_sequence A098861 A098862 
               A098863
%K A098860 nonn,more
%O A098860 1,1
%A A098860 Herman Roelants (herman.roelants(AT)hiw.kuleuven.ac.be), Oct 11 2004

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