

A205647


Numbers n such that 3^n + 16 is prime.


17



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
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OFFSET

1,3


COMMENTS

Indices of primes in A205646.
a(50) > 10^6.  Robert Price, Oct 28 2020


LINKS

Table of n, a(n) for n=1..49.


FORMULA

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


EXAMPLE

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


MATHEMATICA

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


PROG

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


CROSSREFS

Cf. Sequences of numbers n such that 3^n + 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^n + m is also a multiple of 3 (for n greater than 0), and as such isn't prime.
Sequence in context: A187901 A220487 A110133 * A187903 A187839 A183988
Adjacent sequences: A205644 A205645 A205646 * A205648 A205649 A205650


KEYWORD

nonn,hard,more


AUTHOR

Jonathan Vos Post, Jan 30 2012


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, November 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


STATUS

approved



