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%I #19 Sep 02 2022 07:45:01
%S 3,8,13,44,75,88,101,119
%N Numbers of steps until the Collatz iteration started at k > 4 returns to either k-1 or k+1.
%C It is conjectured that no further terms exist.
%C _Michael S. Branicky_ checked this up to 2*10^9 and found no starting values other than the 74 terms given in A355239 and also in the attached file.
%C The terms of this sequence are expected to be close to the sum of numerators and denominators in a rational approximation of log(2)/log(3). See A355514, which shares terms 3, 8, 13, 44, 75.
%H Hugo Pfoertner, <a href="/A355240/a355240.txt">Collatz iterations started at k returning to k+-1</a>.
%o (PARI) a355240(upto) = {my(D=List()); for (start=5, upto, my(old=start,new=0,L=0);while (abs(new-start)>1 && new!=1, L++; if(old%2==0,new=old/2,new=3*old+1);old=new); if(new>1, listput(~D,L))); Set(D)};
%o a355240(10000)
%Y Cf. A005186, A006577, A355514.
%Y A355239 gives the list of starting values.
%Y Cf. A355568, A355569.
%K nonn,more
%O 1,1
%A _Hugo Pfoertner_, Jul 04 2022