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A243147
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Least number k such that n^k + k^n is prime or 0 if no such k exists.
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2
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1, 1, 2, 1, 24, 1, 54, 69, 2, 1, 3100, 1
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OFFSET
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1,3
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COMMENTS
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More terms given in links.
a(n) = 1 if and only if n + 1 is prime. Thus there are infinitely many nonzero entries.
For n in A016767, a(n) = 0 since n^k + k^n is factorable and will never be prime. Thus there are infinitely many zero entries.
If a(i) = j then a(j) <= i for all i and j not equal to 0.
a(n) and n must have opposite parity. If n is odd/even, a(n) must be even/odd, respectively.
Further, gcd(n, a(n)) = 1 for all n.
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LINKS
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EXAMPLE
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3^1 + 1^3 = 4 is not prime. 3^2 + 2^3 = 17 is prime. So a(3) = 2.
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PROG
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(PARI) a(n)=if(ispower(n)&&ispower(n)%3==0&&n%3==0, return(0)); k=1; while(!ispseudoprime(n^k+k^n), k++); return(k)
vector(12, n, a(n))
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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STATUS
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approved
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