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Numbers k such that 5*2^k + 3 is prime.
3

%I #29 Jul 30 2023 10:15:50

%S 1,2,3,4,5,7,8,11,12,18,20,26,28,32,34,43,44,50,52,58,65,66,107,140,

%T 197,274,280,380,393,506,664,738,875,944,1016,1547,1548,1687,3938,

%U 4066,5165,6258,6402,7067,7413,7967,9441,9922,11106,15077,15548,22647,24780,39168,54868

%N Numbers k such that 5*2^k + 3 is prime.

%H Jon Grantham, <a href="/A058586/b058586.txt">Table of n, a(n) for n = 1..74</a>

%H Jon Grantham and Andrew Granville, <a href="https://arxiv.org/abs/2307.07894">Fibonacci primes, primes of the form 2^n-k and beyond</a>, arXiv:2307.07894 [math.NT], 2023.

%F a(n) = A068713(n) + 1.

%t Do[ If[ PrimeQ[ 5*2^n + 3 ], Print[ n ] ], {n, 1, 10000} ]

%o (PARI) is(n)=ispseudoprime(5*2^n+3) \\ _Charles R Greathouse IV_, Jun 12 2017

%Y Cf. A068713.

%K nonn

%O 1,2

%A _Robert G. Wilson v_, Dec 26 2000

%E a(50)-a(53) from _Michael S. Branicky_, Jan 10 2023

%E a(54)-a(74) from _Jon Grantham_, Jul 30 2023