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, 1, 2, 1, 3, 2, 1, 5, 6, 9, 31, 44, 18, 71, 81, 1097, 64, 789, 42, 17, 908, 722, 1500, 1496, 5690, 6720, 3340, 18768, 9597, 13835

Offset

1,3

Comments

These are certified primes using PFGW from Primeform group.

Links

Table of n, a(n) for n=1..30.

Example

3*2^1*(2^2 - 1) - 1 = 17 is prime, as is 19, so k(1)=1 as M(1) = 2^2 - 1;
3*2^1*(2^3 - 1) - 1 = 41 is prime, as is 43, so k(2)=1 as M(2) = 2^3 - 1;
3*2^2*(2^5 - 1) + 1 = 373 is prime, so k(3)=2 as M(3) = 2^5 - 1.

Prog

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

Crossrefs

Cf. A145983.

Sequence in context: A131345 A134423 A061260 * A119442 A064861 A305299

Adjacent sequences: A152094 A152095 A152096 * A152098 A152099 A152100

Keyword

more,nonn

Author

Pierre CAMI, Nov 24 2008

Status

approved