Triangle primes
Jim Nastos
nastos at cs.ualberta.ca
Sat Apr 15 11:12:04 CEST 2006
Hi everyone,
This is a little aside from the 'triangle prime' sequence discussion.
As 7,11,13,29,31 are some consecutive primes expressibe as a sum of two
triangular numbers, I searched the OEIS for this. I found:
A111252 Primes p such that the difference between the closest squares
surrounding p is prime
which is essentially saying that if (n+1)^2 - n^2 is prime, then all
primes between n^2 and (n+1)^2 are in A111252.
Now, since (n+1)^2 - n^2 is just 2n+1, then clearly every odd prime
corresponds to one of these intervals (bounded by consecutive squares) so
clearly, this sequence is infinite...
Note that the entry contains the comment:
Conjecture: The number of terms in this sequence is infinite.
Am I missing something?
Thanks,
J
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