Triangle primes

Jim Nastos nastos at
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?

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