Primes of the form semiprime(a)^semiprime(a) + semiprime(b)^semiprime(b).

[Maximilian Hasler]

Since these numbers grow very fast, it might be technically
preferrable to record the b-values, e.g.

%N Indices m such that A114850(m)+A114850(k) is prime for some k<m.

(with (if there are multiple k's) or without repetition), or the
semiprimes only,

%N Semiprimes M such that M^M+K^K is prime for some semiprime K<M.

? t=0;A001358=vector(100,i,until(bigomega(t++)==2,);t);
? for(i=1,#A001358, for(j=1,i-1,
ispseudoprime(A001358[i]^A001358[i]+A001358[j]^A001358[j]) | next;
print1([i,j]",")))
[6, 1],[9, 1],[9, 2],[19, 5],[20, 8],[25, 7],[33, 11],[38, 6],[40,
33],[59, 14],[69, 62],[76, 57],[99, 22],

Maximilian

On Mon, Apr 28, 2008 at 7:22 AM, Jonathan Post <jvospost3 at gmail.com> wrote:
> Primes of the form semiprime(a)^semiprime(a) + semiprime(b)^semiprime(b).
>
>  Primes of the form A114850(a) + A114850(b).
>
>  a(1) = 437893890380859631 = 256 + 437893890380859375 = 4^4 + 15^15 =
>  semiprime(1)^semiprime(1) + semiprime(6)^semiprime(6).
>
>  a(2) = 88817841970012523233890533447265881 = 256 +
>  88817841970012523233890533447265625 = 4^4 + 25^25 =
>  semiprime(1)^semiprime(1) + semiprime(9)^semiprime(9).
>
>  a(3) =  46656 + 88817841970012523233890533447265625 = 6^6 + 24^25 =
>  semiprime(2)^semiprime(2) + semiprime(9)^semiprime(9).
>
>  Comment: This is to A068145 Primes of the form a^a + b^b as A001358
>  semiprimes is to A000040 primes; and as A114850 (n-th semiprime)^(n-th
>  semiprime) is to A051674 (n-th prime)^(n-th prime).
>
>  Is this right so far?  Would someone like to extend?
>
>  cf. A000040, A001358, A051674, A068145, A114850.
>