A219039 Numbers k such that 3^k - 16 is prime.

3, 5, 11, 15, 51, 69, 99, 227, 381, 537, 9135, 9737, 58437, 105567, 121779, 123645

Offset: 1

Author

Nicolas M. Perrault, Nov 10 2012

Keywords

• nonn
• more

Comments

a(17) > 2*10^5. - Robert Price, Sep 29 2013

Examples

			For k = 3, 3^3 - 16 = 11 and 11 is prime. Hence k = 3 is included in the sequence.
		

Crossrefs

Cf. Sequences of numbers k such that 3^k + m is prime:

(m = 2) A051783, (m = -2) A014224, (m = 4) A058958, (m = -4) A058959,

(m = 8) A217136, (m = -8) A217135, (m = 10) A217137, (m = -10) A217347,

(m = 14) A219035, (m = -14) A219038, (m = 16) A205647, (m = -16) this sequence, (m = 20) A219040, (m = -20) A219041.

Note that if m is a multiple of 3, 3^k + m is also a multiple of 3 (for k greater than 0), and as such isn't prime.

Programs

Mathematica

Do[If[PrimeQ[3^n - 16], Print[n]], {n, 1, 10000}]

PARI

is(n)=isprime(3^n-16) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(13)-a(16) from Robert Price, Sep 29 2013