(PARI)

{

\\ Program generates terms after a(0) only. \\

\\ The purpose of the initial part of it is to \\

\\ determine the number of composites for each \\

\\ partition of the first 20 primes so these are \\

\\ only computed once (along with the product \\

\\ pairs). \\

z=20;C=1;

p=vector(100,n,prime(n));e2=vector(100,n,2^(n-1));

T=matrix(e2[20],2);cm=vector(e2[20]);

for(i=e2[20],e2[21]-1,t=[1,2];b=binary(i);

  for(j=2,20,t[b[j]+1]*=p[j];

    if(j>4,

      if(!ispseudoprime(t[1]+t[2]),

        cm[i-e2[20]+1]++)));

  T[i-e2[20]+1,1]=t[1];T[i-e2[20]+1,2]=t[2]);

while(1,

  i=e2[z];while(i<e2[z+1],

    if(i%e2[z-19]==0,

      while(cm[i/e2[z-19]-e2[20]+1]>C,i+=e2[z-19];

        if(i==e2[z+1],break(2))));

    b=binary(i);c=C+1-cm[i\e2[z-19]-e2[20]+1];f=1;

    t[1]=T[i\e2[z-19]-e2[20]+1,1];

    t[2]=T[i\e2[z-19]-e2[20]+1,2];

    for(j=21,z,t[b[j]+1]*=p[j];

      if(!ispseudoprime(t[1]+t[2]),c--;

        if(!c,i+=e2[z-j+1];f=0;break())));

    if(f,i++;break()));print1("*");

  if(!f,print1(z-1" ");C++);z++)

}

(PARI)

{

\*Auxiliary program generating sequence of primes and composites for (unique) n=13 case*\

a=12178613721830071;t=[1,1];print(2);i=0;while(a,

  i++;t[a%2+1]*=prime(i);s=t[1]+t[2];print1("\n"s);

  if(isprime(s)==0,print1("*"));a\=2);

print1("\n"t)

}