A057026 Smallest prime of form (2n+1)*2^m-1 for some m, or 0 if no such prime exists.

3, 2, 19, 13, 17, 43, 103, 29, 67, 37, 41, 367, 199, 53, 463, 61, 131, 139, 73, 311, 163, 5503, 89, 751, 97, 101, 211, 109, 113, 241663, 487, 251, 1039, 2143, 137, 283, 9343, 149, 307, 157, 647, 331, 2719, 173, 1423, 181, 743, 379, 193, 197, 103423, 823, 419

Offset: 0

Author

Henry Bottomley, Jul 24 2000

Keywords

• nonn

Comments

If a(329) > 0 it is greater than 659*2^10000. - Robert Israel, Jul 01 2014

Indeed, a(329) > 659*2^100000 if it is nonzero. There does not appear to be a covering set, though, so probably a(329) > 0. - Charles R Greathouse IV, Jul 02 2014

a(329) = 659*2^800516 - 1 (found by David W Linton in 2004). - Robert Israel, Jul 04 2014

Examples

			a(5)=43 because 2*5+1=11 and smallest prime of the form 11*2^m-1 is 43 (since 10 and 21 are not prime)
		

Links

• Robert Israel, Table of n, a(n) for n = 0..328
• Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is prime

Crossrefs

Cf. A057024, A057025, A038699.

Programs

Maple

A057026:= proc(n)
local t;
     t:= 2*n;
     while not isprime(t) do t:= 2*t+1 od;
     t
end proc;
seq(A057026(n),n=0..328); # Robert Israel, Jul 01 2014