[seqfan] Re: Prime factor tour

[Chris Thompson]

On Jun 8 2018, Peter Munn wrote:

>With your calculations confirming my first 57 terms (up to the appearance
>of 58), it seems time to tidy my first draft for the sequence and place it
>on OEIS. Please check
>http://oeis.org/draft?user=Peter%20Munn later on Friday. I am not far from
>confirming a(58)=174, having sketched out the sequence to get placings of
>all integers to 149, but only thoroughly checked as far as the appearance
>of 99.

This looks good to me. Go ahead and Propose it for Review.

>>>My hand-calculated terms (with pencilled-in guesses in brackets) are:
>[...]
>> There is a 69 missing between 483 and 23;
>Yes.
>
>> otherwise I can confirm these. I have carried out my own hand
>> calculations up to 90+, and get the following, where the
>> parenthesised values are just one possibility but the positions
>> of the others are determined.
>[...]
>>   76,(152),760,40,
>>   1640,(328,164),82,41,
>>   1783,43,
>>   86,1978,46,
>
>I think your permutation may have missed 42. (Fortunately, I think this
>has only local effects on the terms you have calculated so far: that is no
>effect after the appearance of 46 at least until the appearance of 100.)

How did I manage to leave out 42?! I can only imagine that I was working
in the domain of "All Positive Integers that are not The Answer to
The Ultimate Question of Life, The Universe and Everything" (a sequence
mysteriously absent from OEIS, incidentally).

I agree that only local changes seem to be necessary. Replace 

  1640,(328,164),82,41,
  1783,43,
  86,1978,46,

with

  1640,(328,164),82,41,
  (123,246),1722,42,
  1806,(258),86,43,
  989,1978,46,

-- 
Chris Thompson
Email: cet1 at cam.ac.uk