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Numbers n such that 6^n+5 is prime.
4

%I #23 Feb 11 2021 10:38:06

%S 1,2,4,7,10,14,18,32,55,102,177,190,247,276,372,1524,1545,2502,4966,

%T 5294,13030,13785,14329,27333,44224,93812,127176,128640,136434,184614,

%U 269407,311257,349903,389756

%N Numbers n such that 6^n+5 is prime.

%C a(27) > 10^5. - _Robert Price_, Aug 06 2017

%C As reported by Lelio R Paula in November 2014 at primenumbers.net/prptop, the following three terms are also in this sequence: 127176, 128640, 136434. It is not confirmed that they are the next terms, however. - _Robert Price_, Aug 06 2017

%e 6^1+5=11 and 6^2+5=41, which are both prime, so 1 and 2 are in the sequence. 6^3+5=221 is not prime since it is divisible by 7, so 3 is not in the sequence.

%t Select[Range[0, 100000], PrimeQ[6^# + 5] &] (* _Robert Price_, Aug 06 2017 *)

%o (PARI) is(n)=ispseudoprime(6^n+5) \\ _Charles R Greathouse IV_, Jun 13 2017

%Y Cf. A059614.

%K nonn

%O 1,2

%A _Dmitry Kamenetsky_, Oct 02 2008

%E a(21)-a(26) from _Robert Price_, Aug 06 2017

%E a(27)-a(30) from _Paul Bourdelais_, Jan 28 2021

%E a(31)-a(34) from _Paul Bourdelais_, Feb 11 2021