[seqfan] Behavior of a(n)/a(n-1) in A262765
rselcoe at entouchonline.net
Wed Oct 21 18:22:38 CEST 2015
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?
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