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Search: id:A079321
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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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| 27649, 86400001, 4031078400001, 3319766398771200001, 55696437941726556979200001, 21577941222941856209168026828800001, 215779412229418562091680268288000000000000001
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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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FORMULA
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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))
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PROGRAM
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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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Cf. A002109.
Adjacent sequences: A079318 A079319 A079320 this_sequence A079322 A079323 A079324
Sequence in context: A025309 A097244 A101214 this_sequence A023198 A068404 A023943
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KEYWORD
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easy,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Feb 12 2003
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