A301580 a(n) is the number of positive integers between successive Mersenne primes.

3, 23, 95, 8063, 122879, 393215, 2146959359, 2305843007066210303, 618970017336847128235868159, 162258657859193720701440560726015, 170141021201192402518323912137873817599

Offset: 1

Author

G. L. Honaker, Jr., Mar 23 2018

Keywords

• nonn

Examples

			a(2) = 23 because there are 23 positive integers between successive Mersenne primes 7 and 31.
		

Links

• Caldwell and Honaker, 61897...68159 (27-digits), Prime Curios!

Crossrefs

Cf. A000668, A139231.

Programs

Mathematica

-1 + Differences@ Array[2^MersennePrimeExponent[#] - 1 &, 12] (* Michael De Vlieger, Apr 21 2018 *)

Formula

a(n) = A139231(n) - 1. - Omar E. Pol, Mar 23 2018