A057026 - OEIS

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

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OFFSET

0,1

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

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

EXAMPLE

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)

MAPLE

A057026:= proc(n)

local t;

t:= 2*n;

while not isprime(t) do t:= 2*t+1 od;

end proc;