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A079321
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Composite numbers of the form 1^1 * 2^2 * 3^3 * 4^4 * ... * n^n + 1.
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0
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OFFSET
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1,1
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COMMENTS
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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.
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REFERENCES
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D. E. Knuth, The Art of Computer Programming, Volume 1, 1997, p. 116, problem 7.
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LINKS
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FORMULA
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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)).
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MATHEMATICA
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Select[1+#&/@FoldList[Times, 1, Table[n^n, {n, 10}]], !PrimeQ[#]&] (* Harvey P. Dale, May 02 2011 *)
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PROG
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(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", ")); ) }
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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