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

1,1

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.

Links

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

Formula

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

Example

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).

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 *)

Crossrefs

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

Sequence in context: A046485 A294562 A109377 * A172167 A173060 A173520

Adjacent sequences: A109469 A109470 A109471 * A109473 A109474 A109475

Keyword

nonn

Author

Jonathan Vos Post, Aug 28 2005

Extensions

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

Status

approved