[seqfan] Re: Will this pattern continue for all numbers?

[Hans Havermann]

AS: "The sequence associated with this algorithm is the 'meeting point' for each number (starting from 2): 12, 12, 12, 15, 77, 30, 15, 21, 15, 77, 21, 77, 21, 77, 30, 77, 30, 77, 77, 30, 77, 91, 77, 51, 77, 77, 77, 105" and subsequently acknowledging that a(6) should be 12.

If I'm doing this correctly, I also get different values at a(14), a(19), a(25), and a(28).

RI: "I have verified that for every x from 2 to 6042, F^n(x) eventually hits 60473. However, x=6043 does not. I don't know if F^n(6043) meets the iterates of 2 to 6042: it does not up to F^25464(6043) = 963981399298868702558612537899."

In my sx = {6043, 12086, 18129, 18132, 19643, 19656, 19669, 19682, 20439, 20442, ...} and sy = {6043, 12086, 12088, 13599, 13602, 15869, 15876, 15883, 15890, 16117, ...}, both offset zero, I've got 963981399298868702558612537899 as sx(50928), so clearly I'm counting the in-between numbers as well. With that caveat in mind, I've done a graph of sx (blue) and sy (magenta). There is surprisingly little divergence:

http://chesswanks.com/num/MeetingPoint(6043).png