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A265487
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Numbers k such that 81^k - 9^k - 1 is prime.
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1
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1, 3, 10, 18, 70, 585, 921, 1943, 4635, 13543, 13803, 15938, 39004
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OFFSET
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1,2
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COMMENTS
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For k = 1, 3, 10, 18 the corresponding primes are 71, 530711, 12157665455570144399, 22528399544939174261745512577773519.
a(n) is not of the form 5*k+2 (divisibility by 11), 9*k+2 (divisibility by 19), 7*k+2*(-1)^k+7 (divisibility by 29), 15*k+2 (divisibility by 31) or 29*k+8 (divisibility by 59).
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LINKS
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EXAMPLE
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3 is in the sequence because 81^3 - 9^3 - 1 = 530711 is prime.
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MATHEMATICA
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Select[Range[1000], PrimeQ[81^# - 9^# - 1] &]
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PROG
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(Magma) [n: n in [0..500] | IsPrime(81^n-9^n-1)];
(PARI) for(n=1, 1e3, if(ispseudoprime(81^n - 9^n - 1), print1(n, ", "))) \\ Altug Alkan, Dec 12 2015
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CROSSREFS
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Cf. similar sequences listed in A265481.
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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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