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A350082 Smallest odd number > n with n in its Collatz successors, or 0 if no such odd number exists. a(1) = 1.

%I A350082 #162 Jan 25 2022 09:36:16
%S A350082 1,3,0,5,7,0,9,9,0,11,19,0,17,37,0,17,19,0,25,23,0,25,27,0,33,29,0,37,
%T A350082 33,0,41,75,0,37,41,0,43,39,0,41,109,0,57,51,0,47,55,0,57,133,0,57,55,
%U A350082 0,73,57,0,59,123,0,63,109,0,75,115,0,89,181,0,71,73
%N A350082 Smallest odd number > n with n in its Collatz successors, or 0 if no such odd number exists. a(1) = 1.
%C A350082 a(n) = 0 when n == 0 (mod 3) since such an n has no odd predecessor (only n*2^x). But n !== 0 (mod 3) always has some odd predecessor > n.
%H A350082 Alois P. Heinz, <a href="/A350082/b350082.txt">Table of n, a(n) for n = 1..10000</a>
%H A350082 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%e A350082 a(2) = 3, because 3 is the smallest odd number > 2 that has 2 as a successor: 3 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2.
%e A350082 a(3) = 0 because 3 is not a successor of anything. A060565 contains no 3, nor multiples of 3.
%e A350082 a(11) = 19, because the trajectories of 13, 15, 17 don't contain 11, and 11 is a successor of 19:
%e A350082   13 -> 40..5 -> 16..1;
%e A350082   15 -> 46..23 -> 70..35 -> 106..53 -> 160..5 -> 16..1;
%e A350082   17 -> 52..13;
%e A350082   19 -> 58..29 -> 88..11.
%o A350082 (PARI) a(n)= if(1==n, return(1)); if(!(n%3), return(0)); my(v0=if(n%2, n+2, n+1)); while(1, my(v=v0); while(v>1 && v!=n, v=if(v%2, 3*v+1, v/2)); if(v==n, return(v0)); v0+=2)
%Y A350082 Cf. A060565.
%K A350082 nonn
%O A350082 1,2
%A A350082 _Ruud H.G. van Tol_, Jan 22 2022