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%I #45 Sep 08 2022 08:46:13
%S 1,4,10,34,40,106,418,682,12702,30484,182026,217720,241306
%N Numbers m such that (4^m + 11) / 3 is prime.
%C From _Bruno Berselli_, Aug 26 2015: (Start)
%C After 1, m is always even (for m odd 4^m+11 is divisible by 5).
%C Let m = 2*h. For h = 3*k+1, 9*k+3, 11*k+2, 11*k+8, 13*k+8, 19*k+6, 23*k+10, 23*k+14 and 29*k+28, 4^m+11 is divisible by 9, 37, 89, 23, 53, 229, 47, 1013 and 59, respectively. (End)
%C All terms appear to be of the form 3*k+1. - _Dhilan Lahoti_, Aug 31 2015
%C 12702 is the first counterexample to Dhilan Lahoti's conjecture: 12702 = 3*4234. - _Bruno Berselli_, Feb 02 2017
%C a(14) > 300,000. - _Robert Price_, Mar 18 2017
%e 4 is in the sequence because (4^4+11)/3 = 89 is prime.
%e 10 is in the sequence because (4^10+11)/3 = 349529 is prime.
%t Select[Range[0, 5000], PrimeQ[(4^# + 11)/3] &]
%o (Magma) [n: n in [0..1500] | IsPrime((4^n+11) div 3)];
%o (PARI) is(n)=isprime((4^n + 11) / 3) \\ _Anders Hellström_, Aug 31 2015
%Y Cf. A163868.
%Y Cf. similar sequences listed in A261539.
%K nonn,more
%O 1,2
%A _Vincenzo Librandi_, Aug 26 2015
%E a(9)-a(12) from _Robert Price_, Feb 01 2017
%E a(13) from _Robert Price_, Mar 18 2017
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