|
| |
|
|
A079321
|
|
Composite numbers of the form 1^1*2^2*3^3*4^4*...n^n + 1.
|
|
0
| |
|
|
27649, 86400001, 4031078400001, 3319766398771200001, 55696437941726556979200001, 21577941222941856209168026828800001, 215779412229418562091680268288000000000000001
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| No primes other than 2,5,109 found in this sequence for n <= 1000. 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+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)+1 is Composite. Exp(ln(1) + 2ln(2) + 3ln(3) + ... kln(k)) = exp(Sum(k*ln(k), k=1..n))
|
|
|
MATHEMATICA
| Select[1+#&/@FoldList[Times, 1, Table[n^n, {n, 10}]], !PrimeQ[#]&] (* From Harvey P. Dale, May 02 2011 *)
|
|
|
PROG
| (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
| Cf. A002109.
Sequence in context: A097244 A101214 A202589 * A023198 A204831 A190111
Adjacent sequences: A079318 A079319 A079320 * A079322 A079323 A079324
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Cino Hilliard (hillcino368(AT)gmail.com), Feb 12 2003
|
| |
|
|
