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Search: id:A057856
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| A057856 |
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Least k such that (n+1)^k + n^k is a prime. |
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3
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| 1, 1, 1, 2, 1, 1, 2, 1, 1, 32, 1, 2, 4, 1, 1, 4, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 4
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Note: k must be of the form 2^m (see A058064 for the m values).
Conjecture: For all pairs of relative prime numbers (x, y) there exists at least one number n=2^m and one prime number p such p=x^n+y^n. This sequence show one case of this conjecture where y=x+1. - Tomas Xordan (xordan.tom(AT)gmail.com), Jun 02 2007
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EXAMPLE
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a(101)=16 because 101^16+102^16 = 254536435001431070450581794495937
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MATHEMATICA
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Do[ k = 0; While[ !PrimeQ[ (n + 1)^(2^k) + n^(2^k) ], k++ ]; Print[ 2^k ], {n, 1, 60} ].
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CROSSREFS
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Cf. A130536.
Sequence in context: A068696 A133009 A053734 this_sequence A117939 A105522 A131774
Adjacent sequences: A057853 A057854 A057855 this_sequence A057857 A057858 A057859
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KEYWORD
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hard,nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 14 2000
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