A355239 - OEIS

%I #24 Oct 17 2022 11:51:43

%S 5,6,7,9,11,14,15,17,18,19,25,33,39,41,47,51,54,57,59,62,71,81,89,91,

%T 107,108,121,159,161,166,183,243,250,252,284,333,376,378,411,432,487,

%U 501,639,649,651,667,865,889,959,975,977,1153,1185,1299,1335,1368,1439,1731,1779,1823,2159,2307,2430,2735,3239,3643,4103,4617,4857,4859,6155,7287,7289,9233

%N Starting values k > 4 of a Collatz iteration reaching either k-1 or k+1.

%C No further terms up to 2*10^9. It is conjectured that this is the full list of starting values of Collatz trajectories reaching k-1 or k+1, and that the number of steps until this happens is one of the 8 terms of A355240.

%C There are no further terms up to 31100000000. - _Dmitry Kamenetsky_, Oct 17 2022

%H Hugo Pfoertner, <a href="/A355239/a355239.txt">Upward and downward steps in Collatz orbits started at k returning to k+-1, sorted by orbit lengths</a>, (2022).

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

%o (Python)

%o def f(x): return 3*x+1 if x%2 else x//2

%o def ok(n):

%o     if n < 5: return False

%o     ni, targets = n, {1, n-1, n+1}

%o     while ni not in targets: ni = f(ni)

%o     return ni in {n-1, n+1}

%o print([k for k in range(10**4) if ok(k)]) # _Michael S. Branicky_, Jul 04 2022

%Y Cf. A070991, A070993, A355240, A355568, A355569.

%K nonn

%O 1,1

%A _Hugo Pfoertner_, Jul 04 2022