A135434 a(n) is the smallest odd number that makes a(n)*2^N(n)-1 prime, where N(n) is the n-th Mersenne number that makes 2^N(n)-1 prime.

3, 3, 7, 3, 9, 7, 51, 15, 69, 19, 25, 103, 1905, 273, 139, 13, 4027, 3619, 2187, 3211, 6621, 1897, 17461, 2511, 90579, 30189, 805, 86539, 30091, 317917, 198681, 755061, 1283911, 26869, 1564347, 4348099, 383731, 6020095

Offset: 1

Author

Lei Zhou, Dec 13 2007

Keywords

• nonn
• hard
• more

Comments

First 22 terms are obtained by Mathematica. Terms from 23 to 38 are obtained by Jean Penna's LLR program.

Examples

			First Mersenne number N(1)=2, 2^2-1=3 is the first Mersenne prime. 3*2^2-1=11 is prime;
Fifth Mersenne number N(5)=13, 2^13-1=8191 is the fifth Mersenne prime. 9*2^13-1=73727 is prime.
		

Links

• Jean Penna, LLR.
• Lei Zhou, Prime page

Crossrefs

Cf. A000043.

Extensions

a(35)-a(37) from Pierre CAMI, Apr 06 2015

a(38) from Lei Zhou, Sep 04 2022