Sequence Derived From Coprimality
Leroy Quet
qqquet at mindspring.com
Wed Dec 4 00:35:25 CET 2002
(sent to sci.math as well)
Let a[1] = 1;
Let, for n >= 2, a[n] be the minimum positive integer not equal to
(a[1],a[2],...a[n-1]), where GCD(a[n],a[m]) = 1 for all m where
ceiling(n/2) <= m <= n-1.
This sequence begins (I think, figured by hand):
1, 2, 3, 5, 4, 7, 9, 11, 13, 17, 8, 19, 23, 25, ...
This may be easy to prove, actually, but is this sequence
made up only of powers of primes?
Is there a direct means of generating the sequence?
Anything else? (such as, is this sequence a rearrangement of the
prime-powers?)
Thanks,
Leroy Quet
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