minesweeper sequences
murthy amarnath
amarnath_murthy at yahoo.com
Sun Mar 19 14:50:45 CET 2006
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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