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 A152097 Least k(n) such that 3*2^k(n)*M(n)-1 or 3*2^k(n)*M(n)+1 is prime (or both primes) with M(i)=i-th Mersenne prime. 1

%I

%S 1,1,2,1,3,2,1,5,6,9,31,44,18,71,81,1097,64,789,42,17,908,722,1500,

%T 1496,5690,6720,3340,18768,9597,13835

%N Least k(n) such that 3*2^k(n)*M(n)-1 or 3*2^k(n)*M(n)+1 is prime (or both primes) with M(i)=i-th Mersenne prime.

%C These are certified primes using PFGW from Primeform group.

%e 3*2^1*(2^2 - 1) - 1 = 17 is prime, as is 19, so k(1)=1 as M(1) = 2^2 - 1;

%e 3*2^1*(2^3 - 1) - 1 = 41 is prime, as is 43, so k(2)=1 as M(2) = 2^3 - 1;

%e 3*2^2*(2^5 - 1) + 1 = 373 is prime, so k(3)=2 as M(3) = 2^5 - 1.

%o (PARI) /* these functions are too slow for n > about 15 */

%o mersenne(n) = {local(i,m);i=n;m=1;while(i>0,m=m+1;if(isprime(2^m-1),i=i-1));2^m-1}

%o A152097(n) = {local(k,m);k=1;m=mersenne(n);while(!(isprime(3*2^k*m-1)||isprime(3*2^k*m+1)),k=k+1);k} \\ _Michael B. Porter_, Mar 18 2010

%Y Cf. A145983.

%K more,nonn

%O 1,3

%A _Pierre CAMI_, Nov 24 2008

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Last modified September 24 13:43 EDT 2021. Contains 347643 sequences. (Running on oeis4.)