minesweeper sequences

[franktaw at netscape.net]

It's not an unreasonable concept.  But please don't overdo it.  Two 
examples (maybe primes and squares) would be quite sufficient.  It 
would be definitely more interesting if you can prove (for a particular 
case) that every "unmined" number is reached, and/or that every natural 
number is used as a "jump" size.

Also, before you do something like this, you want to look at a simpler 
case, if one exists.  In this case, one does: don't mine anything.  
This gives us A081145.  You should certainly reference this from your 
new sequences.

Incidently, A100709 is very similar to A081145.  I think it should be 
identical (except for the offset).  The first difference is at n=13 (or 
12), where A100709 has 28, while A081145 has 27.  From the definition, 
A100709 should be 27 there, too.

Franklin T. Adams-Watters

-----Original Message-----
From: murthy amarnath <amarnath_murthy at yahoo.com>

  Neil and seq. fans,
does the following make sense?
 Mine sweeper sequence.
Let there be mines under prime numbers in the sequence
of natural numbers ( on the number line).
A man starts from 1 and moves on the line to cover all
composite numbers once. Each time he  can take a jump
of length k only once for every k. he can take a jump
on either side. He moves so that he gives priority to
touch the smallest composite number not covered
earlier.
   Beginning with 1  he takes a jump of 3 to touch 4
then a jump of 2 to touch 6 , then a jump of 4 to
touch 10 then a jump of 1 in the other direction to
touch 9 and so on.
The sequence is
1,4,6,10,9,14,8,15,24,12,20,...
the 'k' seq is
3,2,4,1,5,6,7,9,12,8,...

More such sequences can be defined  if the mines are
placed under other well known sequences.
thanks
amarnath murthy



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