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A079322
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Composite numbers of the form 1^1*2^2*3^3*4^4*...n^n + 11.
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0
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12, 15, 119, 27659, 86400011, 4031078400011, 3319766398771200011, 55696437941726556979200011, 21577941222941856209168026828800011, 215779412229418562091680268288000000000000011
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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.
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REFERENCES
| D. E. Knuth, The Art of Computer Programming, Volume 1 1997 p 116 problem 7
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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))
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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", ")); ) }
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CROSSREFS
| Sequence in context: A109315 A024875 A152190 * A167304 A191966 A135451
Adjacent sequences: A079319 A079320 A079321 * A079323 A079324 A079325
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KEYWORD
| easy,nonn
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AUTHOR
| Cino Hilliard (hillcino368(AT)gmail.com), Feb 12 2003
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