A205647 Numbers k such that 3^k + 16 is prime.

0, 1, 3, 4, 7, 8, 9, 12, 13, 15, 27, 31, 49, 57, 60, 75, 139, 147, 283, 327, 488, 604, 700, 825, 908, 1051, 1064, 1215, 5319, 9669, 10136, 16675, 25656, 28933, 35864, 47671, 68028, 73380, 186223, 194965, 221649, 233059, 240644, 513007, 543128, 551491, 648872, 989124, 994536

Offset: 1

Author

Jonathan Vos Post, Jan 30 2012

Keywords

• nonn
• hard
• more

Comments

Indices of primes in A205646.

a(50) > 10^6. - Robert Price, Oct 28 2020

Examples

			57 is in the sequence because (3^57) + 16 = 1570042899082081611640534579 is prime.
		

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

Select[Range[0, 2000], PrimeQ[3^# + 16] &] (* T. D. Noe, Jan 30 2012 *)

PARI

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

Formula

{n: 3^n + 16 is in A000040} = {n: 3^n + 16 is prime} = {n: A000244(n) is prime} = {n: A205646(n) is prime}.

Extensions

5319 from Nicolas M. Perrault, Nov 10 2012

a(30)-a(40) from Robert Price, Oct 23 2013

a(41) discovered by Lelio R Paula, Nov 2016

a(42)-a(43) from Robert Price, Apr 02 2020

a(44)-a(46) from Robert Price, May 14 2020

a(47)-a(49) from Robert Price, Oct 28 2020