A219051 Numbers k such that 3^k - 34 is prime.

4, 7, 11, 13, 29, 32, 36, 44, 79, 157, 197, 341, 467, 996, 1421, 2479, 3269, 5203, 7987, 9341, 14836, 26047, 47816, 64304, 100693, 127597, 167167, 174697, 182089, 198791

Offset: 1

Author

Nicolas M. Perrault, Nov 10 2012

Keywords

• nonn
• more

Comments

a(31) > 2*10^5. - Robert Price, Nov 23 2013

Examples

			For k = 4, 3^4 - 34 = 47 and 47 is prime. Hence k = 4 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) A219039,

(m = 20) A219040, (m = -20) A219041, (m = 22) A219042, (m = -22) A219043,

(m = 26) A219044, (m = -26) A219045, (m = 28) A219046, (m = -28) A219047,

(m = 32) A219048, (m = -32) A219049, (m = 34) A219050, (m = -34) A219051. 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 - 34], Print[n]], {n, 1, 10000}]
Select[Range[10000], PrimeQ[3^# - 34] &] (* Alonso del Arte, Nov 10 2012 *)

PARI

is(n)=isprime(3^n-34) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(21)-a(30) from Robert Price, Nov 23 2013