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A265482
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Numbers n such that 16^n - 4^n - 1 is prime.
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1
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1, 2, 5, 9, 19, 25, 54, 104, 112, 120, 177, 317, 504, 540, 734, 780, 1649, 1923, 2715, 4308, 5917, 6494, 7305, 22653, 26888, 71448, 93834, 137027, 158472, 174648
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OFFSET
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1,2
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COMMENTS
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For n = 1, 2, 5, 9, 19, 25, the corresponding primes are 11, 239, 1047551, 68719214591, 75557863725639445512191, 1267650600228228275596796362751.
a(n) is not of the form 5*k+6 (divisibility by 11) or 9*k+8 (divisibility by 19) or 7*k+3*(-1)^k (divisibility by 29).
Conjecture: the odd terms are not of the form 8*k+7.
n is in the sequence iff 2*n is in A098845 (terms a(21)-a(30) are derived from that sequence). - Ray Chandler, Sep 25 2019
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LINKS
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EXAMPLE
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5 is in the sequence because 16^5-4^5-1 = 1047551 is prime.
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MATHEMATICA
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Select[Range[2500], PrimeQ[16^# - 4^# - 1] &]
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PROG
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(Magma) [n: n in [0..500] | IsPrime(16^n-4^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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STATUS
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approved
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