A355240 Numbers of steps until the Collatz iteration started at k > 4 returns to either k-1 or k+1.

3, 8, 13, 44, 75, 88, 101, 119

Offset: 1

Author

Hugo Pfoertner, Jul 04 2022

Keywords

• nonn
• more

Comments

It is conjectured that no further terms exist.

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.

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.

Links

• Hugo Pfoertner, Collatz iterations started at k returning to k+-1.

Crossrefs

Cf. A005186, A006577, A355514.

A355239 gives the list of starting values.

Cf. A355568, A355569.

Programs

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)};
a355240(10000)