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 A265482 Numbers n such that 16^n - 4^n - 1 is prime. 1

%I #16 Sep 08 2022 08:46:14

%S 1,2,5,9,19,25,54,104,112,120,177,317,504,540,734,780,1649,1923,2715,

%T 4308,5917,6494,7305,22653,26888,71448,93834,137027,158472,174648

%N Numbers n such that 16^n - 4^n - 1 is prime.

%C For n = 1, 2, 5, 9, 19, 25, the corresponding primes are 11, 239, 1047551, 68719214591, 75557863725639445512191, 1267650600228228275596796362751.

%C 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).

%C Conjecture: the odd terms are not of the form 8*k+7.

%C 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

%e 5 is in the sequence because 16^5-4^5-1 = 1047551 is prime.

%t Select[Range[2500], PrimeQ[16^# - 4^# - 1] &]

%o (Magma) [n: n in [0..500] | IsPrime(16^n-4^n-1)];

%o (PARI) is(n)=ispseudoprime(16^n-4^n-1) \\ _Charles R Greathouse IV_, Jun 13 2017

%Y Cf. A098845, similar sequences listed in A265481.

%K nonn,more

%O 1,2

%A _Vincenzo Librandi_, Dec 10 2015

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Last modified June 21 20:04 EDT 2024. Contains 373559 sequences. (Running on oeis4.)