A109472 Cumulative sum of primes p such that 2^p - 1 is a Mersenne prime.

2, 5, 10, 17, 30, 47, 66, 97, 158, 247, 354, 481, 1002, 1609, 2888, 5091, 7372, 10589, 14842, 19265, 28954, 38895, 50108, 70045, 91746, 114955, 159452, 245695, 356198, 488247, 704338, 1461177, 2320610, 3578397, 4976666, 7952887, 10974264, 17946857, 31413774, 52409785, 76446368, 102411319, 132813776, 165396433, 202553100, 245196901, 288309510

Offset: 1

Author

Jonathan Vos Post, Aug 28 2005

Keywords

• nonn

Comments

Prime cumulative sum of primes p such that 2^p - 1 is a Mersenne prime include: a(1) = 2, a(2) = 5, a(4) = 17, a(6) = 47, a(8) = 97, a(14) = 1609, a(18) = 10589. After 1, all such indices x of prime a(x) must be even.

Examples

			a(1) = 2, since 2^2-1 = 3 is a Mersenne prime.
a(2) = 2 + 3 = 5, since 2^3-1 = 7 is a Mersenne prime.
a(3) = 2 + 3 + 5 = 10, since 2^5-1 = 31 is a Mersenne prime.
a(4) = 2 + 3 + 5 + 7 = 17, since 2^7-1 = 127 is a Mersenne prime; 17 itself is prime (in fact a p such that 2^p-1 is a Mersenne prime).
a(18) = 2 + 3 + 5 + 7 + 13 + 17 + 19 + 31 + 61 + 89 + 107 + 127 + 521 + 607 + 1279 + 2203 + 2281 + 3217 = 10589 (which is prime).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..48 (terms 1..47 from Gord Palameta)

Crossrefs

Cf. A000043, A000668 for the Mersenne primes, A001348, A046051, A057951-A057958.

Programs

Mathematica

Accumulate[Select[Range[3000], PrimeQ[2^# - 1] &]] (* Vladimir Joseph Stephan Orlovsky, Jul 08 2011 *)
Accumulate@ MersennePrimeExponent@ Range@ 45 (* Michael De Vlieger, Jul 22 2018 *)

Formula

a(n) = Sum_{i=1..n} A000043(i).

Extensions

a(38)-a(47) from Gord Palameta, Jul 21 2018