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

1,1

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

Table of n, a(n) for n=1..8.

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

Prog

(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)

Crossrefs

Cf. A005186, A006577, A355514.

A355239 gives the list of starting values.

Cf. A355568, A355569.

Sequence in context: A066809 A009848 A337504 * A355514 A281267 A346054

Adjacent sequences: A355237 A355238 A355239 * A355241 A355242 A355243

Keyword

nonn,more

Author

Hugo Pfoertner, Jul 04 2022

Status

approved