[seqfan] Another Collatz-like algorithm

[Ali Sada]

Hi Everyone,

 

Please seethe algorithm below.

 

1. Pick aninteger n>0

2. If n iseven, divide by 2. If n is odd, find the least triangular number T greater thenn and add n+T.

3. Repeatstep 2. with either n/2 or n+T

 

Other thanthe powers of 2, the numbers I tested take one of two routes:

 
a.      They go into loops that have5 at their lowest point.Ex. 31+36=67; 67+78=145; 145+153=298; 298/2=149; 149+153=302;302/2=151; 151+153=304; 304/16=19; 19+21=40; 40/8=5.5+6=11; 11+15=26; 26/2=13; 13+15=28; 28/4=7; 7+10=17; 17+21=38; 38/2=19; 19+21=40; 40/8=5.

 

b.      They go up to a point wherethe software doesn’t work anymore. Maybe they go up to infinity, but I cannotconfirm. Ex.173, 285, 331, etc. 

 

Can we provethat numbers in the second category actually go to infinity? And if so, would theybe an interesting sequence?

 

Best,

 

Ali