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%I #10 Sep 23 2018 20:58:12
%S 2,1,3,3,2,2,4,3,4,1,3,4,3,3,5,4,4,3,5,8,2,2,4,3,4,2,4,4,4,4,6,3,4,3,
%T 5,8,4,4,6,5,6,1,3,3,3,3,5,8,4,3,6,6,3,3,5,4,5,3,5,5,5,5,7,8,4,4,5,8,
%U 5,4,6,8,6,3,5,5,6,5,7,8,6,5,8,7,2,2,4,3,4,2,4,4,4,4,6,8,6,3,5,5,4,4,7,5,6
%N Let f be defined as in A159885. Then a(n) = max{A000120(f^i(2n+1)): 1 <= i <= A159885(n)}.
%C Problem: find an upper estimate for a(n).
%H Antti Karttunen, <a href="/A159945/b159945.txt">Table of n, a(n) for n = 1..65537</a>
%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%o (PARI)
%o A006519(n) = (1<<valuation(n, 2));
%o f(n) = ((3*((n-1)/2))+2)/A006519((3*((n-1)/2))+2); \\ Defined for odd n only. Cf. A075677.
%o A159945(n) = { my(w=hammingweight(n), m = 0, n = (n+n+1)); for(k=1,oo,n = f(n); m = max(m,hammingweight(n)); if(hammingweight(n) <= w, return(m))); }; \\ _Antti Karttunen_, Sep 22 2018
%Y Cf. A000120, A006519, A007814, A075677, A159885.
%K nonn
%O 1,1
%A _Vladimir Shevelev_, Apr 27 2009
%E More terms from _Antti Karttunen_, Sep 22 2018
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