cp's OEIS Frontend

A213209 Number of isolated even numbers in Collatz (3x+1) trajectory of n.

%I A213209 #19 May 01 2025 17:35:56
%S A213209 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 A213209 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 A213209 2,3,3,0,0,2,21,2,24,3,1,2,1,6,5,0,2,24,23,0
%N A213209 Number of isolated even numbers in Collatz (3x+1) trajectory of n.
%C A213209 An isolated even is not a member of any even chain in Collatz trajectory of n; see also A213181.
%H A213209 T. D. Noe, <a href="/A213209/b213209.txt">Table of n, a(n) for n = 1..10000</a>
%F A213209 From _Alan Michael Gómez Calderón_, Apr 23 2025: (Start)
%F A213209 a(n) = a(A139391(n)) + A133872(n+2) for n >= 2;
%F A213209 a(n) = A286380(n) - A213181(n). (End)
%e A213209 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 A213209 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 A213209 Cf. A133872, A139391, A213181, A286380.
%K A213209 nonn
%O A213209 1,6
%A A213209 _Jayanta Basu_, Mar 02 2013