login
Starting from sigma(n), number of halving steps to reach 1 in '3x+1' problem, or -1 if this never happens.
5

%I #9 Feb 16 2020 17:35:55

%S 0,5,2,11,6,7,3,12,7,14,7,13,12,8,8,67,14,23,6,7,5,15,8,14,67,7,7,14,

%T 13,16,5,68,9,71,9,59,15,14,14,13,7,10,12,8,24,16,9,69,22,13,16,18,71,

%U 15,16,15,8,13,14,9,68,10,10,31,8,17,11,69,10,17,16,76,16,23,69,12,10,9,8,14,61,69,8,16,72,20,15,14,13,16,15,9,7,17

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

%H Antti Karttunen, <a href="/A332452/b332452.txt">Table of n, a(n) for n = 1..8192</a>

%H Antti Karttunen, <a href="/A332452/a332452.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) = A006666(A000203(n)).

%F a(n) = A332209(n) - A332453(n).

%o (PARI)

%o A006666(n) = { my(t); while(n>1, if(n%2, n=3*n+1, n>>=1; t++)); (t); }; \\ From A006666

%o A332452(n) = A006666(sigma(n));

%Y Cf. A000203, A006666, A332209, A332453, A332454.

%K nonn

%O 1,2

%A _Antti Karttunen_, Feb 16 2020