[seqfan] Re: Concatenate distances from n to prevprime and nextprime
franktaw at netscape.net
franktaw at netscape.net
Mon Jan 11 18:10:34 CET 2010
If you check up to 10000, you can pretty sure that you've found all the
loops. Based on prime distribution, after that , you're going to get
the next term smaller than the current one.
A number that maps to itself would be considered a size 1 loop, not
size 0.
Franklin T. Adams-Watters
-----Original Message-----
From: Eric Angelini <Eric.Angelini at kntv.be>
Hello seqFans,
dp = (n-prevprime)
dn = (nextprime-n)
we could now concatenate dp and dn and iterate from there,
this concatenation being the new 'n'.
We'll get for instance, starting with n = 94:
dp = (94-prevprime) = (94-89) = 5
dn = (nextprime-94) = (97-94) = 3
new 'n' = 53
etc.
We'll have 94->53->66->51->42->11->42...
11-42 is the first loop I get, the only second one being:
15-22-31-26-33-24-15...
(if all this is not cooked)
I've looked for a 3rd loop -- but couldn't find any, in the
range n=1 to 1000. Is there a possible 3rd loop somewhere?
If not, a first seq could be formed by the integers which
end in loop #1 -- they are about 70% less than the ones which
end in loop #2.
Best,
É.
BTW, could it be that the concatenation of dp & dn gives back
the starting n? (a size-zero loop)?
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