A319535 - OEIS

%I #31 Jan 25 2024 12:18:35

%S 11,71,431,2591,15551,4353564671,5642219814911,341163456359156416511,

%T 2046980738154938499071,20628849596981071092343898111,

%U 26734989077687468135677691953151,207891275068097752223029732627709951,269427092488254686881046533485512097791

%N Primes of the form 2*6^k - 1.

%C Primes in A164559.

%C Companion sequence of A057472. There are 49 terms known in this sequence.

%H K. D. Bajpai, <a href="/A319535/b319535.txt">Table of n, a(n) for n = 1..26</a>

%F a(n) = 2*6^A057472(n) - 1.

%e 2*6^1 - 1 = 11, 2*6^2 - 1 = 71, 2*6^3 - 1 = 431, 2*6^4 - 1 = 2591 and 2*6^5 - 1 = 15551 are primes, but 2*6^6 - 1 = 93311 = 23*4057 is not.

%p A319535:= n-> (2*6^n-1): select(isprime, [seq((A319535(n), n=1..200))]);  # _K. D. Bajpai_, Nov 15 2019

%t Select[Table[2*6^k-1,{k,1600}], PrimeQ[#]&]  (* _K. D. Bajpai_, Nov 15 2019 *)

%o (PARI) for(n=1, 99, my(t); if(ispseudoprime(t=2*6^n-1), print1(t", ")))

%o (Magma) [k: n in [1..100] | IsPrime(k) where k is 2*6^n-1];  // _K. D. Bajpai_, Nov 15 2019

%Y Integers k such that 2*b^k - 1 is prime: A090748 (b=2), A003307 (b=3), A120375 (b=5), A057472 (b=6), A002959 (b=7), A002957 (b=10), A120378 (b=11).

%Y Primes of the form 2*b^k - 1: A000668 (b=2), A079363 (b=3), A120376 (b=5), this sequence (b=6), A158795 (b=7), A055558 (b=10), A120377 (b=11).

%Y Cf. also A000043, A002958, A068231, A164559.

%K nonn

%O 1,1

%A _Jianing Song_, Sep 22 2018