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A127837
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Numbers n such that ((n+1)^n-1)/n^2 is a prime.
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3
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OFFSET
| 1,1
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COMMENTS
| All terms are primes. Corresponding primes of the form ((n+1)^n-1)/n^2 are listed in A128466(n) = {2, 7, 311, 7563707819165039903, ...}.
It seems that if p is in the sequence then the first three numbers n such that n^2 divides (p+1)^n-1 are: 1, p & ((p+1)^p-1)/p. 2 is in the sequence and the first three terms of A127103 are : 1, 2 & ((2+1)^2-1)/2; 3 is in the sequence and the first three terms of A127104 are : 1, 3 & ((3+1)^3-1)/3; 5 is in the sequence and the first three terms of A127106 are : 1, 5 & ((5+1)^5-1)/5.
No other terms below 20000. - Max Alekseyev (maxale(AT)gmail.com), Apr 25 2007
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EXAMPLE
| 4357 is in the sequence because (4358^4357-1)/4357^2 is prime.
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CROSSREFS
| Cf. A128466, A037205, A060072, A060073, A058128, A128456, A127103, A127104, A127106, A128398.
Sequence in context: A099936 A092506 A127063 * A004249 A121510 A132346
Adjacent sequences: A127834 A127835 A127836 * A127838 A127839 A127840
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KEYWORD
| hard,more,nonn
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AUTHOR
| Farideh Firoozbakht (mymontain(AT)yahoo.com) and Alexander Adamchuk (alex(AT)kolmogorov.com), Mar 13 2007
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