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%I #23 Apr 16 2013 12:38:39
%S 5,5,5,13,9,5,13,5,9,5,17,9,13,13,5,9,21,9,9,17,0,5,9,5,13,13,13,13,
%T 17,5,9,9,0,9,9,13,13,5,17,17,17,17,17,17,21,9,5,5,25,13,5,0,25,13,13,
%U 17,9,5,13,9,33,9,9,0,0,21,9,33,21,9,13,5,13,9,17
%N Number of cycles the reduced complex Collatz function using 3 + (2n-1)i takes to hit 1 + i, or 0 if this never happens.
%C The complex Collatz function takes a complex number z to 3iz + (1+i). The resulting real part is divided by 2 until it's odd, and the same for the imaginary part.
%C The effect here is that say 4 + 14i is reduced to 1 + 7i.
%C The reduced complex Collatz function does all this in the same cycle.
%C Equals 0 for n = 21, 33, 52, 64, 65, 81, 82, 101, 103, 127, 129, 130, 163, 201, 204, 206, 253, 254...
%C This is conjectured to be infinite and the same as in A224067.
%C For example, 3 + 41i yields -61 + 5i, -7 + -91i, 137 + -5i, 1 + 103i, -77 + 1i, -1 + -115i, 173 + -1i, 1 + 65i, -97 + 1i, -1 + -145i, 109 + -1i, 1 + 41i, -61 + 1i, -1 + -91i, 137 + -1i, 1 + 103i, -77 + 1i, -1 + -115i, 173 + -1i, 1 + 65i, -97 + 1i, -1 + -145i, 109 + -1i, 1 + 41i, which becomes cyclic about 1 + 41i.
%H Eric Weisstein, <a href="http://mathworld.wolfram.com/CollatzProblem.html">Mathworld: Collatz Problem</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Collatz_conjecture">Collatz Problem</a>
%e a(5) = 13 because rcC(3 + 7i) yields -5 + 5i, -7 + -7i, 11 + -5i, 1 + 17i, -25 + 1i, -1 + -37i, 7 + -1i, 1 + 11i, -1 + 1i, -1 + -1i, 1 + -1i, 1 + 1i, which is 13 terms.
%o (JavaScript)
%o for (b=1;b<150;b+=2) {
%o c=1;
%o r[0]=3;i[0]=b;
%o while (r[c-1]!=1 || i[c-1]!=1 && c<1000) {
%o i[c]=r[c-1]*3+1;
%o r[c]=-i[c-1]*3+1;
%o while (r[c]%2==0) r[c]/=2;
%o while (i[c]%2==0) i[c]/=2;
%o c++;
%o }
%o document.write(c+", ");
%o }
%Y Cf. A224067.
%K nonn,less
%O 1,1
%A _Jon Perry_, Apr 02 2013
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