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 A218797 #14 Nov 06 2012 11:12:40
%S A218797 0,0,0,1,0,1,2,1,2,0,1,2,2,1,3,2,3,1,2,1,1,2,2,2,1,2,1,2,4,1,3,2,2,2,
%T A218797 2,2,2,4,3,3,3,2,4,4,3,0,2,1,1,1,1,2,2,3,2,4,4,3,3,2,3,4,2,2,3,2,1,3,
%U A218797 3,1,2,2,5,1,4,2,2,1,1,6,3,1,5,1,1,5,4,1,4,1,2,6,2,4,2,2,2,1,4,4
%N A218797 Number of ways to write 2n - 1 as p + q + r with p <= q <= r and p, q, r, p^2 + q^2 + r^2 all prime.
%C A218797 Conjecture: a(n) > 0 for all n=1715,1716,....
%C A218797 This conjecture is stronger than the weak Goldbach conjecture. It has been verified for n up to 500,000. Those 0<n<1715 with a(n)=0 are 1, 2, 3, 5, 10, 46, 126, 129, 154, 201, 385, 426, 475, 1714.
%H A218797 Zhi-Wei Sun, <a href="/A218797/b218797.txt">Table of n, a(n) for n = 1..10000</a>
%e A218797 a(7)=2 since 13=3+3+7=3+5+5, and both 3^2+3^2+7^2=67 and 3^2+5^2+5^2=59 are primes.
%t A218797 a[n_]:=a[n]=Sum[If[PrimeQ[n-Prime[j]-Prime[k]]==True&&PrimeQ[Prime[j]^2+Prime[k]^2+(n-Prime[j]-Prime[k])^2]==True,1,0],{j,1,PrimePi[n/3]},{k,j,PrimePi[(n-Prime[j])/2]}]
%t A218797 Do[Print[n," ",a[2n-1]],{n,1,10000}]
%Y A218797 Cf. A000040, A054860, A085317, A218754, A218585, A218654, A218656.
%K A218797 nonn
%O A218797 1,7
%A A218797 _Zhi-Wei Sun_, Nov 05 2012