cp's OEIS Frontend

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

%I A205647 #37 Jul 06 2025 22:30:41
%S A205647 0,1,3,4,7,8,9,12,13,15,27,31,49,57,60,75,139,147,283,327,488,604,700,
%T A205647 825,908,1051,1064,1215,5319,9669,10136,16675,25656,28933,35864,47671,
%U A205647 68028,73380,186223,194965,221649,233059,240644,513007,543128,551491,648872,989124,994536
%N A205647 Numbers k such that 3^k + 16 is prime.
%C A205647 Indices of primes in A205646.
%C A205647 a(50) > 10^6. - _Robert Price_, Oct 28 2020
%F A205647 {n: 3^n + 16 is in A000040} = {n: 3^n + 16 is prime} = {n: A000244(n) is prime} = {n: A205646(n) is prime}.
%e A205647 57 is in the sequence because (3^57) + 16 = 1570042899082081611640534579 is prime.
%t A205647 Select[Range[0, 2000], PrimeQ[3^# + 16] &] (* _T. D. Noe_, Jan 30 2012 *)
%o A205647 (PARI) is(n)=isprime(3^n+16) \\ _Charles R Greathouse IV_, Feb 17 2017
%Y A205647 Cf. Sequences of numbers k such that 3^k + m is prime:
%Y A205647   (m = 2) A051783, (m = -2) A014224, (m = 4) A058958, (m = -4) A058959,
%Y A205647   (m = 8) A217136, (m = -8) A217135, (m = 10) A217137, (m = -10) A217347,
%Y A205647   (m = 14) A219035, (m = -14) A219038, (m = 16) A205647, (m = -16) A219039,
%Y A205647   (m = 20) A219040, (m = -20) A219041, (m = 22) A219042, (m = -22) A219043,
%Y A205647   (m = 26) A219044, (m = -26) A219045, (m = 28) A219046, (m = -28) A219047,
%Y A205647   (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.
%K A205647 nonn,hard,more
%O A205647 1,3
%A A205647 _Jonathan Vos Post_, Jan 30 2012
%E A205647 5319 from _Nicolas M. Perrault_, Nov 10 2012
%E A205647 a(30)-a(40) from _Robert Price_, Oct 23 2013
%E A205647 a(41) discovered by Lelio R Paula, Nov 2016
%E A205647 a(42)-a(43) from _Robert Price_, Apr 02 2020
%E A205647 a(44)-a(46) from _Robert Price_, May 14 2020
%E A205647 a(47)-a(49) from _Robert Price_, Oct 28 2020