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A180362
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Primes of the form k * n^n + 1 with k < n^n.
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2
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5, 13, 109, 163, 257, 271, 379, 433, 487, 541, 769, 3329, 7681, 7937, 9473, 10753, 11777, 12289, 13313, 14081, 14593, 15361, 17921, 18433, 19457, 22273, 23041, 23297, 25601, 26113, 26881, 30977, 31489, 32257, 36097, 36353, 37501, 37633, 37889, 39937, 40193
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OFFSET
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1,1
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COMMENTS
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A result of Heath-Brown shows, on the GRH, that this sequence is infinite; can this be proved unconditionally? The averaged result of Bombieri-Friedlander-Iwaniec does not seem to be strong enough.
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LINKS
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FORMULA
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k * n^n + 1, where k < n^n.
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EXAMPLE
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a(4) = 109, because 4 * 3^3 + 1 = 109, which is prime, and 4 < 27.
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PROG
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(PARI) isA180362(n)=my(b=2); while(b^b<n, if(n%(b^b)==1 && n < b^(2*b), return(isprime(n))); b++); 0
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Kevin Batista (kevin762401(AT)yahoo.com), Aug 30 2010, Sep 01 2010
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EXTENSIONS
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STATUS
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approved
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