duplicate hunting, pt. 7
Ray Chandler
rayjchandler at sbcglobal.net
Sat Apr 28 17:25:27 CEST 2007
>
> Possible duplicates:
>
> A075643 and A076074
>
> -Andrew Plewe-
>
I don't have a proof, but have convinced myself that these two sequences continue to agree. The first term of a group
is essentially the least number not previously included. The previous groups have sieved out multiples of earlier
numbers. After 2*prime(k)+1 groups have been selected, there are no non-primes available less than prime(k)^2. It
takes one more group for A076074 since we don't have complete freedom to choose the last two terms of a group, but the
same argument holds. The least number available continues to be prime, a(n) = prime(n-1) for n>2. These sequences turn
out to be the non-composites (A008578) with the first two terms transposed.
Ray Chandler
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