A213209 - OEIS

%I #14 Mar 04 2013 21:43:30

%S 0,1,1,0,0,2,2,0,2,1,1,1,0,3,3,0,0,3,2,0,0,2,2,1,2,1,24,2,1,4,23,0,2,

%T 1,1,2,2,3,5,0,23,1,3,1,0,3,22,1,2,3,2,0,0,25,24,2,3,2,4,3,2,24,24,0,

%U 2,3,3,0,0,2,21,2,24,3,1,2,1,6,5,0,2,24,23,0

%N Number of isolated even numbers in Collatz (3x+1) trajectory of n.

%C An isolated even is not a member of any even chain in Collatz trajectory of n; see also A213181.

%H T. D. Noe, <a href="/A213209/b213209.txt">Table of n, a(n) for n = 1..10000</a>

%e a(7)=2 since there are only 2 numbers 22 and 34 in the Collatz trajectory of 7 that are not part of any even chain.

%t Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; Table[c = Collatz[n]; cnt = 0; evenCnt = 0; Do[If[OddQ[i], If[evenCnt == 1, cnt++]; evenCnt = 0, evenCnt++], {i, c}]; cnt, {n, 100}] (* _T. D. Noe_, Mar 02 2013 *)

%Y Cf. A213181.

%K nonn

%O 1,6

%A _Jayanta Basu_, Mar 02 2013