login
A355240
Numbers of steps until the Collatz iteration started at k > 4 returns to either k-1 or k+1.
5
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.
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
A355239 gives the list of starting values.
Sequence in context: A066809 A009848 A337504 * A355514 A281267 A346054
KEYWORD
nonn,more
AUTHOR
Hugo Pfoertner, Jul 04 2022
STATUS
approved