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A265481
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Numbers k such that 9^k - 3^k - 1 is prime.
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9
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1, 2, 3, 6, 7, 20, 35, 36, 140, 523, 1170, 1731, 1842, 3727, 3886, 9270, 11071, 13823, 14451, 27086, 27606, 31876, 78008
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OFFSET
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1,2
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COMMENTS
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For k = 1, 2, 3, 6, 7, 20, 35, the corresponding primes are 5, 71, 701, 530711, 4780781, 12157665455570144399, 2503155504993241551284026887086141.
a(n) is not of the form 4*k+5 (divisibility by 5) or 5*k+4 (divisibility by 11) or 9*k+4*(-1)^k (divisibility by 19).
Conjectures: a(n) is not of the form 7*k+4 or 8*k.
a(17) = 11071 mod 7 is 4, so the first half of the conjecture above is not true. - Robert Price, Sep 25 2019
a(23) = 78008 is divisible by 8, so the second half of the conjecture above is not true. - Robert Price, Sep 25 2019
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LINKS
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EXAMPLE
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6 is in the sequence because 9^6 - 3^6 - 1 = 530711 is prime.
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MATHEMATICA
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Select[Range[1500], PrimeQ[9^# - 3^# - 1] &]
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PROG
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(Magma) [n: n in [0..500] | IsPrime(9^n-3^n-1)];
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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