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

[Jonathan Post]

Thank you, Maximilian Hasler!

That is excellent. I agree with the compression in your suggested
presentation.  It does leave a conjecture as to whether there are
values with repetition after M = 9.

My presentation was made, however, not to optimize presentation of
this sequence, but for the parallels based on the semiprime:prime
analogue.

Also, that we have the related:

(3) primes of the form semiprime(a)^semiprime(a) +
semiprime(b)^semiprime(b) + semiprime(c)^semiprime(c);

(4) primes of the form semiprime(a)^semiprime(a) +
semiprime(b)^semiprime(b) + semiprime(c)^semiprime(c) +
semiprime(d)^semiprime(d);

and so forth.

These in turn are subsets of the seqs:

(2) primes of the form a^a + b^b;

(3) primes of the form a^a + b^b + c^c;

(4) primes of the form a^a + b^b + c^c + d^d;

and so forth which, as I recall, go up to the 6th of that
supersequence, for which I gave the Mathematica code.

You're also right to search first for pseudoprimality, and then test
the candidates for primality.  I did so with Factoris in the short
email as first posted, for which you shall have full credit for the
extension and the code.  I'll need to consider if your presentation is
superior and, if so, how to best show the analogues.

For the next 3 days, as with all Mondays, Tuesdays, and Wednesdays
through the school year (i.e. until late June) I teach high school
math for 8 hours, roughly 7:30 a.m.-3:30 p.m., then rush from Pasadena
to Los Angeles for graduate courses towards my full teaching
credentials.  That I've been adjunct professor and teacher in other
venues on and off since 1974 makes the credential-quest seem silly,
but the 3 consecutive 14-hour days (including commute time) means that
I'm not going to deluge seqfans or OEIS as much as when I'd more time
on my hands.

Hence thank you again for helping me with these more select sequences,
as I meander from quantity towards quality.

Best,

Jonathan Vos Post

p.s. several friends of mine were evacuated safely from the Sierra
Madre fires about 5 miles to the East of here, which made it to being
the lead story in tonight's national NBC-TV news.  They say that the
fire is 30% contained, and may run to mid-week.  All classes in all
Sierra Madre schools have been canceled for Monday.

On 4/27/08, Maximilian Hasler <maximilian.hasler at gmail.com> wrote:
> 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.
>  >
>