A176559 The number of primes between two consecutive Mersenne primes.

1, 6, 19, 996, 11222, 31138, 105054174, 55890483939986569, 10201730748372641087928204

Offset: 1

Author

G. L. Honaker, Jr., Dec 07 2010

Keywords

• nonn
• hard
• more

Examples

			a(3) = 19 because between 3rd and fourth Mersenne primes (31 and 127) there are 19 primes (37, 41, 43, ... 113).
		

Links

• G. L. Honaker, Jr. and C. Caldwell, 19, Prime Curios!.

Crossrefs

Cf. A000040, A000668 (Mersenne primes), A059305.

Programs

Mathematica

(* Run the program for A000668 first *) Table[-1 + PrimePi[A000668[[n + 1]]] - PrimePi[A000668[[n]]], {n, 7}] (* Alonso del Arte, Dec 07 2010 *)
PrimePi[#[[2]]]-PrimePi[#[[1]]]&/@Partition[2^MersennePrimeExponent[Range[8]]-1,2,1]-1 (* The program generates the first 7 terms of the sequence. *) (* Harvey P. Dale, Jul 31 2025 *)

Formula

a(n) = A059305(n+1) - A059305(n) - 1. - Amiram Eldar, May 14 2023

Extensions

a(9) from the data at A059305 added by Amiram Eldar, May 14 2023