A227230 Numbers k such that 3*2^k + {5,7} are twin primes.

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

Offset: 1

Author

Zak Seidov, Sep 20 2013

Keywords

• nonn
• more
• hard

Comments

No more terms up to 10^4.

Any subsequent terms exceed 200,000. - Lucas A. Brown, Sep 02 2024

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

Links

• Jon Grantham and Andrew Granville, Fibonacci primes, primes of the form 2^n-k and beyond, arXiv:2307.07894 [math.NT], 2023.

Crossrefs

Intersection of A057913 and A059746. - Jason Yuen, Sep 02 2024

Cf. A071558, A181490.

Programs

Mathematica

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

PARI

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