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Numbers k such that 3*2^k + {5,7} are twin primes.
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%I #22 Sep 08 2024 09:26:00

%S 1,2,3,5,6,19,22

%N Numbers k such that 3*2^k + {5,7} are twin primes.

%C No more terms up to 10^4.

%C Any subsequent terms exceed 200,000. - _Lucas A. Brown_, Sep 02 2024

%C Any subsequent terms exceed 10^6, by non-primality of 3*2^k+7 for members of b-file at A057913 > 22 and table in Section 6 of Grantham and Granville link. - _Michael S. Branicky_, Sep 07 2024

%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.

%t Reap[Do[If[PrimeQ[a=3*2^n+5]&&PrimeQ[a+2],Sow[n]],{n,150}]][[2,1]]

%o (PARI) for(k = 1,10^4, if(ispseudoprime(a = 3*2^k + 5)&&ispseudoprime (a + 2), print1(k",")))

%Y Intersection of A057913 and A059746. - _Jason Yuen_, Sep 02 2024

%Y Cf. A071558, A181490.

%K nonn,more,hard

%O 1,2

%A _Zak Seidov_, Sep 20 2013