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A328660
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Numbers k such that (10^k + 7^k)/17 is prime.
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0
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OFFSET
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1,1
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COMMENTS
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All terms are odd primes. Proof: a(n) cannot be even, because (10^(2*k) + 7^(2*k))/17 is not an integer. If odd number k = x*y, then (10^x + 7^x) and (10^y + 7^y) are nontrivial factors of (10^(x*y) + 7^(x*y)). In conclusion, a(n) must be odd and prime. - Daniel Suteu, Jan 22 2020
The corresponding primes are 79, 6871, 5998666279, 588905817363845479, ...
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LINKS
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MATHEMATICA
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Select[Table[Prime[n], {n, 500}], PrimeQ[(10^#+7^#)/17] &] (* Modified by Jinyuan Wang, Jan 22 2020 *)
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PROG
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(PARI) forprime(k=3, 10000, if(isprime((10^k+7^k)/17), print1(k, ", ")))
(Magma) [p: p in PrimesUpTo(1000) | IsPrime((10^p+7^p) div 17)]; // Modified by Jinyuan Wang, Jan 22 2020
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CROSSREFS
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KEYWORD
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nonn,more,hard
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AUTHOR
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STATUS
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approved
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