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Starting from sigma(n), number of tripling steps to reach 1 in '3x+1' problem, or -1 if 1 is never reached.
5

%I #9 Feb 16 2020 17:36:02

%S 0,2,0,5,2,2,0,5,2,6,2,5,5,2,2,39,6,11,1,1,0,6,2,5,39,1,1,5,5,6,0,39,

%T 2,41,2,33,6,5,5,4,1,2,4,1,11,6,2,39,10,4,6,7,41,5,6,5,1,4,5,1,39,2,2,

%U 15,1,6,3,39,2,6,6,43,6,10,39,3,2,1,1,4,34,39,1,5,41,8,5,4,4,5,5,1,0,6,5,39,7,45,11,7,7,41,2,12,2

%N Starting from sigma(n), number of tripling steps to reach 1 in '3x+1' problem, or -1 if 1 is never reached.

%H Antti Karttunen, <a href="/A332453/b332453.txt">Table of n, a(n) for n = 1..8192</a>

%H Antti Karttunen, <a href="/A332453/a332453.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = A006667(A000203(n)).

%F a(n) = A332209(n) - A332452(n).

%o (PARI)

%o A006667(n) = { my(t=0); while(n>1, if(n%2, t++; n=3*n+1, n>>=1)); (t); };

%o A332453(n) = A006667(sigma(n));

%Y Cf. A000203, A006667, A332209, A332452, A332455.

%K nonn

%O 1,2

%A _Antti Karttunen_, Feb 16 2020