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 A209253 #19 Jul 23 2020 04:19:20
%S A209253 0,1,1,2,2,2,2,2,2,2,2,3,2,3,3,4,3,5,2,3,4,4,4,5,2,3,5,2,4,7,4,2,6,2,
%T A209253 5,6,2,2,6,1,3,7,4,3,7,4,5,8,2,3,8,3,3,8,4,4,7,4,5,8,3,4,7,1,5,9,5,3,
%U A209253 9,3,4,8,4,3,9,3,5,8,2,2,9,4,3,8,4,4,10,1,3,10,5,4,10,4,3,9,5,5,10,4
%N A209253 Number of ways to write 2n-1 as the sum of a Sophie Germain prime and a practical number.
%C A209253 Conjecture: a(n)>0 for all n>1.
%C A209253 This has been verified for n up to 5*10^6.
%H A209253 Zhi-Wei Sun, <a href="/A209253/b209253.txt">Table of n, a(n) for n = 1..10000</a>
%H A209253 Zhi-Wei Sun, <a href="http://arxiv.org/abs/1211.1588">Conjectures involving primes and quadratic forms</a>, arxiv:1211.1588 [math.NT], 2012-2017
%e A209253 a(40)=1 since 2*40-1=23+56 with 23 a Sophie Germain prime and 56 a practical number.
%t A209253 f[n_]:=f[n]=FactorInteger[n]
%t A209253 Pow[n_,i_]:=Pow[n,i]=Part[Part[f[n],i],1]^(Part[Part[f[n],i],2])
%t A209253 Con[n_]:=Con[n]=Sum[If[Part[Part[f[n],s+1],1]<=DivisorSigma[1,Product[Pow[n,i],{i,1,s}]]+1,0,1],{s,1,Length[f[n]]-1}]
%t A209253 pr[n_]:=pr[n]=n>0&&(n<3||Mod[n,2]+Con[n]==0)
%t A209253 a[n_]:=a[n]=Sum[If[PrimeQ[2Prime[k]+1]==True&&pr[2n-1-Prime[k]]==True,1,0],{k,1,PrimePi[2n-1]}]
%t A209253 Do[Print[n," ",a[n]],{n,1,100}]
%Y A209253 Cf. A005384, A005153, A208243, A208244, A208246, A208249.
%K A209253 nonn
%O A209253 1,4
%A A209253 _Zhi-Wei Sun_, Jan 14 2013