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A248031
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Least number k such that k^n +- k +- 1 is prime for all four possibilities, or 0 if no such k exists.
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0
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3, 15, 6, 0, 30594, 246819, 0, 4033590, 2298429, 0, 19209840, 13542816, 0, 3979836, 75524874, 0, 143635866, 220808901, 0, 14557221, 185958081, 0, 180438825, 320588085, 0, 499478574, 29105421, 0, 37340766, 1169275746, 0, 2051928486, 27069021, 0, 971311320
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OFFSET
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2,1
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COMMENTS
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a(19) > 155*10^6.
For n == 2 (mod 3), k^n + k + 1 is divisible by k^2 + k + 1. Thus, for n > 2, if n == 2 (mod 3), a(n) = 0.
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LINKS
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PROG
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(PARI)
a(n)=if(n>2&&n==Mod(2, 3), return(0)); k=1; while(!ispseudoprime(k^n+k+1)||!ispseudoprime(k^n+k-1)||!ispseudoprime(k^n-k+1)||!ispseudoprime(k^n-k-1), k++); k
n=2; while(n<100, print1(a(n), ", "); n++)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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