A079321 Composite numbers of the form 1^1 * 2^2 * 3^3 * 4^4 * ... * n^n + 1.

27649, 86400001, 4031078400001, 3319766398771200001, 55696437941726556979200001, 21577941222941856209168026828800001, 215779412229418562091680268288000000000000001

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.

Links

Table of n, a(n) for n=1..7.

Formula

Prod(k^k, k=1..n)+1 is Composite. Exp(log(1) + 2log(2) + 3log(3) + ... klog(k)) = exp(Sum(k*log(k), k=1..n)).

Mathematica

Select[1+#&/@FoldList[Times, 1, Table[n^n, {n, 10}]], !PrimeQ[#]&] (* 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: A101214 A339257 A202589 * A251235 A023198 A230608

Adjacent sequences: A079318 A079319 A079320 * A079322 A079323 A079324

Keyword

easy,nonn

Author

Cino Hilliard, Feb 12 2003

Status

approved