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

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

Offset: 1

Author

Vincenzo Librandi, Dec 10 2015

Keywords

• nonn
• more

Comments

For k = 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.

k is in the sequence iff 2*k is in A098845 (terms a(21)-a(30) are derived from that sequence). - Ray Chandler, Sep 25 2019

Examples

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

Crossrefs

Cf. A098845, similar sequences listed in A265481.

Programs

Magma

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

Mathematica

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

PARI

is(n)=ispseudoprime(16^n-4^n-1) \\ Charles R Greathouse IV, Jun 13 2017