Wednesday, 15 January 2025

Collatz Trajectory Crossing Records

One of the properties associated with my diurnal age's number (27681) is that it is a member of OEIS A319738:


 A319738Numbers whose Collatz trajectories cross their initial values a record number of times.

The initial members of the sequence are: 1, 3, 6, 9, 14, 18, 33, 54, 97, 129, 194, 257, 294, 313, 342, 353, 398, 417, 470, 626, 9225, 13739, 14473, 19297, 27681, 38881 (permalink)

Table 1 shows the progressive records (permalink):


Table 1

Figure 1 shows the Collatz trajectory of 27681 in which there are 61 crossings (permalink):


Figure 1

These record crossings are rather rare and I don't know if I'll experience the next one. I'll be 38881 days old which I'm unlikely to reach. The reason that I've never encountered these record number of crossings before is that the previous one occurred when I was 
19297 days old, long before I started this daily number analysis.

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