%I #14 Apr 02 2017 10:14:10

%S 6,10,12,18,30,34,36,130,132,514,131074

%N Numbers of form p^i + p^j for at least two values of p prime and i, j > 0.

%C 2*F is in the sequence, where F is a Fermat prime.

%C a(12) (if it exists) > 2*10^9. - _Giovanni Resta_, Apr 02 2017

%e 10 = 2^3 + 2^1 = 5^1 + 5^1.

%e 30 = 3^3 + 3^1 = 5^2 + 5^1.

%e 132 = 2^7 + 2^2 = 11^2 + 11^1.

%o (PARI) limit=L; v=vector(limit); for(n=1,limit,forprime(p=2,n/2,for(k=1,logint(n\2,2),for(j=k,logint(n,2),forprime(q=p+1,n/2,for(t=1,logint(n\2,3),for(u=t,logint(n,3),if(n-p^k==p^j&&n-q^t==q^u,v[n]=1)))))))); for(n=1,limit,if(v[n],print1(n", ")))

%Y Cf. A019434, A246655, A284665.

%K nonn,more

%O 1,1

%A _Gionata Neri_, Mar 31 2017