[seqfan] Concatenate distances from n to prevprime and nextprime

[Eric Angelini]

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)?