[seqfan] Re: A055198 comment seems wrong

Hans Havermann gladhobo at bell.net
Fri Mar 18 17:07:25 CET 2022

Maximilian: "... This shows that there are 22 new cycles here, respectively represented by all odd numbers from 1011 to 1053. The next cycle contains only numbers larger than 10000."

Each of those new cycles contains 90 terms, so we have now a b-file of 90*22+54 terms:


I think that the author's assertion that "all integers <= 10000" iterate to a cycle of the first 54 might have been a typo: 10000 = 1000. That's a lot easier than looking for some definitional issue or programming mishap. His "99889" maximum for the 111 trajectory can be understood by treating half-iteration (+4 without the digits-reversal) results as part of the domain (although clearly not part of the trajectory since he states the correct number of iterations).

Why posit the conjecture without attempting some four-digit evolutions which would have revealed the additional cycles? Perhaps because (in its long run) the trajectory of 111 runs into plenty of both four- and five-digit integers that end up in the 54-cycle.

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