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A261539 Numbers m such that (4^m + 5) / 3  is prime. 4

%I

%S 0,1,2,3,6,9,12,21,42,150,195,390,411,1215,2754,2757,3246,6186,11340,

%T 12885,84708,87120,191772,503919,786441

%N Numbers m such that (4^m + 5) / 3 is prime.

%C After 1, m is not of the form 3*k+1 because in this case 4^m+5 is divisible by 9; after 2, m is not of the form 3*k+2 because in this case 4^m+5 is divisible by 7. Therefore, m>2 is always a multiple of 3. - _Bruno Berselli_, Aug 25 2015

%C Larger members of the sequence generate probable primes only. - _Serge Batalov_, Aug 27 2015

%H Henri & Renaud Lifchitz PRPtop, <a href="http://www.primenumbers.net/prptop/searchform.php?form=%282%5En%2B5%29%2F3&amp;action=Search">(2^n+5)/3 PRPs</a>

%e 6 is in the sequence because (4^6+5)/3 = 1367 is prime.

%e 9 is in the sequence because (4^9+5)/3 = 87383 is prime.

%e 4 is not in the sequence because (4^4+5)/3 = 87 = 3*29 is not prime.

%t Select[Range[0, 5000], PrimeQ[(4^# + 5)/3] &]

%o (MAGMA) [n: n in [0..1000] | IsPrime((4^n+5) div 3)];

%o (PARI) isok(n)=isprime((4^n + 5) / 3) \\ _Anders Hellström_, Aug 25 2015

%Y Cf. A163834.

%Y Cf. numbers n such that (4^n+k)/3 is prime: this sequence (k=5), A261577 (k=11), A261578 (k=17), A261579 (k=23).

%Y Cf. A253772.

%K nonn,more

%O 1,3

%A _Vincenzo Librandi_, Aug 25 2015

%E a(18)-a(23) from Lelio R Paula (2012-2014) via _Serge Batalov_, Aug 27 2015

%E a(24)-a(25) from _Serge Batalov_, Aug 29 2015

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Last modified January 27 17:58 EST 2020. Contains 331296 sequences. (Running on oeis4.)