|
Search: id:A079322
|
|
|
| A079322 |
|
Composite numbers of the form 1^1*2^2*3^3*4^4*...n^n + 11. |
|
+0
1
|
|
| 12, 15, 119, 27659, 86400011, 4031078400011, 3319766398771200011, 55696437941726556979200011, 21577941222941856209168026828800011, 215779412229418562091680268288000000000000011
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
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.
|
|
REFERENCES
|
D. E. Knuth, The Art of Computer Programming, Volume 1 1997 p 116 problem 7
|
|
FORMULA
|
Prod(k^k, k=1..n)+11 is Composite. Exp(ln(1) + 2ln(2) + 3ln(3) + ... kln(k)) = exp(Sum(k*ln(k), k=1..n))
|
|
PROGRAM
|
(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", ")); ) }
|
|
CROSSREFS
|
Sequence in context: A109315 A024875 A152190 this_sequence A167304 A135451 A143090
Adjacent sequences: A079319 A079320 A079321 this_sequence A079323 A079324 A079325
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Cino Hilliard (hillcino368(AT)gmail.com), Feb 12 2003
|
|
|
Search completed in 0.002 seconds
|
