[seqfan] Behavior of a(n)/a(n-1) in A262765

Bob Selcoe rselcoe at entouchonline.net
Wed Oct 21 18:22:38 CEST 2015

Hello Seqfans,

A262765: a(n) = the number of ways that at least two distinct primes <= 
prime(n) sum to a prime.

The plot for a(n)/a(n-1) was extended today from n=400 to n=500 (BTW – the 
entry  shows the Table as n=2..500 but it’s still only to 400, so that 
needs to be fixed); the extension suggests my conjecture may be tenuous or 
false about a(n)/a(n-1) tending to increase (in the manner described in the 
Oct. 20 comment).

But the more interesting questions are whether or not the ratio remains 
proximal to 2 as n increases, and whether it tends to remain < 2.

Does anyone have any insight about any of these questions?  Any way to 
calculate a range (say, for n>250) or a limit?  Since I can’t program, might 
somebody assist in extending the plot?

Bob Selcoe

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