[seqfan] Iteration of k -> sigma(k)-1

Neil Sloane njasloane at gmail.com
Fri Sep 22 15:10:55 CEST 2017


Dear Seq Fans,
According to Richard Guy, Erdos conjectured that the trajectory of n under
that map always reaches a prime. A039654 gives the prime reached, or -1 (I
changed the escape value to make it consistent with similar sequences),
and A039655 gives no. of steps.
I just created A292112 and -3 for the records in A039654. They need b-files.
The record values in A039655 appear to match A073485, but surely that is
just a coincidence, so could someone please compute more terms? The
positions of the records in A039655 is the new A292114.

In other words, the records in the present b-file for A039655 are [0, 2, 5,
6, 7, 11, 13, 15, 17] - how does this continue?
The positions of the records are [2, 4, 9, 121, 301, 441, 468, 3171, 8373]
which is now A292114. How does this continue, and what ARE these numbers?

A039655 could use a bigger b-file, or an a-file with 100,000 or more terms.



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