A331217 a(n) is the least prime of the form 2^m - 2^n - 1.

2, 5, 3, 7, 47, 31, 191, 127, 16127, 3583, 15359, 6143, 1044479, 8191, 245759, 16744447, 4128767, 131071, 786431, 524287, 274876858367, 14680063, 4398042316799, 260046847, 4278190079, 4261412863, 1125899839733759, 576460752169205759, 16911433727

Offset: 0

Author

Hugo Pfoertner, Jan 12 2020

Keywords

• nonn

Examples

			a(1) = 2: 2^2 - 2^0 - 1 = 2, thus exponent 2 = A181692(0);
a(2) = 5: 2^3 - 2^1 - 1 = 5, 2^2 - 2^1 - 1 = 1 is not a prime, A181692(1) = 3;
a(4) = 47: 2^6 - 2^4 - 1 = 31, whereas the first candidate 2^5 - 2^4 - 1 = 15 is composite.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..680

Crossrefs

Cf. A181692 (corresponding values of m), A331204, A331205.

Programs

Magma

a:=[]; for n in [0..30] do m:=n+1; while not IsPrime(2^m-2^n-1) do m:=m+1; end while; Append(~a,2^m-2^n-1); end for; a; // Marius A. Burtea, Jan 13 2020

Maple

f:= proc(n) local m, p;
   p:= -1;
   for m from n do
     p:= p + 2^m;
     if isprime(p) then return p fi
    od
end proc:
map(f, [$0..30]); # Robert Israel, Jan 13 2020

Mathematica

a[n_] := For[m = n+1, True, m++, If[PrimeQ[p = 2^m-2^n-1], Return[p]]];
a /@ Range[0, 28] (* Jean-François Alcover, Oct 25 2020 *)

PARI

for(n=0,28, for(m=n+1,oo, k=2^m-2^n-1; if(isprime(k), print1(k,", "); break)))