Sequence & Its Terms' Differences
Leroy Quet
qqquet at mindspring.com
Sun Mar 9 01:55:09 CET 2003
In general, I am wondering if there are any known examples (ie. in the
OEIS) of sequences which are permutations of the positive integers, and
also the absolute-values of the differences between their adjacent terms
also form permutations of the positive integers.
So, the {a(1),a(2),a(3),....} is a permutation of the positive integers
(ie. the sequence is made of only positive integers, where each positive
integer occurs once and only once somewhere in the sequence),
and the sequence {|a(2)-a(1)|,|a(3)-a(2)|,|a(4)-a(3)|,...} is also a
permutation of the positive integers.
--
Specifically, does the following sequence (interesting either way) fall
into the above category? (Also, the difference-sequence is interesting to
me either way.)
a(1) = 1;
For m >= 2,
a(m) = lowest positive integer not in {a(1),a(2),...,a(m-1)} such that
|a(m) -a(m-1)| is a positive integer not in
{|a(2)-a(1)|,|a(3)-a(2)|,...,|a(m-1)-a(m-2)|}.
I get these sequences (calculated by hand...unsure of correctness):
a(k) -> 1, 2, 4, 7, 3, 8, 14, 5, 12, 20, 6,...
difference-> 1, 2, 3, 4, 5, 6, 9, 7, 8, 14,...
(Not apparently in the OEIS.)
Thanks,
Leroy Quet
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