A176559 The number of primes between two consecutive Mersenne primes.

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

Offset

1,2

Links

Table of n, a(n) for n=1..9.

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

Formula

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

Example

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

Mathematica

(* Run the program for A000668 first *) Table[-1 + PrimePi[A000668[[n + 1]]] - PrimePi[A000668[[n]]], {n, 7}] (* Alonso del Arte, Dec 07 2010 *)

Crossrefs

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

Sequence in context: A091876 A041066 A060748 * A241715 A224919 A282377

Adjacent sequences: A176556 A176557 A176558 * A176560 A176561 A176562

Keyword

nonn,hard,more

Author

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

Extensions

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

Status

approved