%I
%S 0,1,1,1,1,2,3,1,4,2,3,2,2,4,2,1,3,5,4,2,1,4,2,2,5,3,17,4,4,3,16,1,6,
%T 4,2,5,4,5,6,2,17,2,6,4,4,3,16,2,5,6,5,3,2,18,17,4,7,5,6,3,3,17,15,1,
%U 6,7,5,4,3,3,16,5,18,5,2,5,5,7,6,2,4,18,17,2,1,7,5,4,6,5,14,3,3,17,15,2,19
%N Number of oddtheneven runs to reach 1 under the modified `3x+1' map: n > n/2 if n is even, n > (3n+1)/2 if n is odd.
%C The 2>1 step is not counted.
%e 7>11>17>26>13>20>10>5>8>4>2>1, so the oddtheneven runs are (7>11>17>26) (13>20>10) (5>8>4>2), and a(7) is 3.
%t Table[Length[Split[Most[NestWhileList[T, i, #!=1&]], OddQ[ #1]EvenQ[ #2]]], {i, 1, 100}]
%K nonn
%O 1,6
%A Brenton Bostick (bostick(AT)gmail.com), May 18 2009
