%I #13 Dec 15 2021 07:50:25
%S 12,15,119,27659,86400011,4031078400011,3319766398771200011,
%T 55696437941726556979200011,21577941222941856209168026828800011,
%U 215779412229418562091680268288000000000000011
%N Composite numbers of the form 1^1 * 2^2 * 3^3 * 4^4 * ... * n^n + 11.
%C No primes of this form in the sequence for n <= 60. Conjecture: There are no primes in the sequence 2^2 * 3^3 * 4^4 * ... * n^n + 1 for n > 3. Conjecture: There are no primes in the sequence 2^2 * 3^3 * 4^4 * ... * n^n + 11 for all n. Conjecture: There are no primes in the sequence 2^2 * 3^3 * 4^4 * ... * n^n + 61 for all n.
%C There are no primes of this form for n <= 3800. - _Michael S. Branicky_, Dec 15 2021
%D D. E. Knuth, The Art of Computer Programming, Volume 1, 1997, p. 116, problem 7.
%H Michael S. Branicky, <a href="/A079322/b079322.txt">Table of n, a(n) for n = 1..37</a>
%F Prod(k^k, k=1..n) + 11 is composite. Exp(log(1) + 2log(2) + 3log(3) + ... klog(k)) = exp(Sum(k*log(k), k=1..n)).
%t Select[Table[Product[k^k,{k,n}]+11,{n,10}],CompositeQ] (* _Harvey P. Dale_, Jun 12 2016 *)
%o (PARI) pcomposits(n,b) = { for(x=1,n, p=1; for(y=1,x, p = p*(y^y); ); if(!isprime(p+b),print1(p+b",")); ) }
%o (Python)
%o from sympy import isprime
%o from itertools import count
%o def agen():
%o p = 1
%o for k in count(1):
%o p *= k**k
%o if not isprime(p + 11):
%o yield p + 11
%o g = agen()
%o print([next(g) for n in range(1, 12)]) # _Michael S. Branicky_, Dec 15 2021
%K easy,nonn
%O 1,1
%A _Cino Hilliard_, Feb 12 2003