This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A204580 #14 Feb 17 2025 08:17:47
%S A204580 1,2,3,4,5,6,8,10,12,15,15,17,20,24,27,30,32,32,34,36,39,41,43,46,50,
%T A204580 51,54,60,64,68,71,76,78,80,83,86,92,93,98,101,104,106,109,113,114,
%U A204580 117,126,128,133,135,139,143,147,150,160,166,173,181
%N A204580 Number of primes of the form A204142[i]*A204142[j]+2 (i,j <= n), larger than A204142[n].
%C A204580 It is not yet known whether there is a finite number of "good numbers" A204142. This is equivalent to the question whether this sequence will eventually decrease to zero.
%C A204580 One has a(100)=408, a(316)=2179, a(1000)=13136, a(3162)=86603, a(10000)=609377.
%H A204580 M. F. Hasler, <a href="/A204580/b204580.txt">Table of n, a(n) for n = 1..3000</a>
%o A204580 (PARI) A204580(n)={ my(r=1,s); while( A204142[r]^2+2<=A204142[n], r++); s=r; sum(i=r,n, while(s>1 & A204142[s-1]*A204142[i]+2 > A204142[n],s--); sum(j=s,i, is/*pseudo*/prime(A204142[j]*A204142[i]+2)))} /* From n~3000 on, use of ispseudoprime is significantly faster. The vector A204142 must be already computed. */
%K A204580 nonn
%O A204580 1,2
%A A204580 _M. F. Hasler_, Feb 11 2012