A109472 - OEIS

%I #21 Aug 06 2018 05:22:03

%S 2,5,10,17,30,47,66,97,158,247,354,481,1002,1609,2888,5091,7372,10589,

%T 14842,19265,28954,38895,50108,70045,91746,114955,159452,245695,

%U 356198,488247,704338,1461177,2320610,3578397,4976666,7952887,10974264,17946857,31413774,52409785,76446368,102411319,132813776,165396433,202553100,245196901,288309510

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

%C 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.

%H Gord Palameta, <a href="/A109472/b109472.txt">Table of n, a(n) for n = 1..47</a>

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

%e a(1) = 2, since 2^2-1 = 3 is a Mersenne prime.

%e a(2) = 2 + 3 = 5, since 2^3-1 = 7 is a Mersenne prime.

%e a(3) = 2 + 3 + 5 = 10, since 2^5-1 = 31 is a Mersenne prime.

%e 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).

%e a(18) = 2 + 3 + 5 + 7 + 13 + 17 + 19 + 31 + 61 + 89 + 107 + 127 + 521 + 607 + 1279 + 2203 + 2281 + 3217 = 10589 (which is prime).

%t Accumulate[Select[Range[3000], PrimeQ[2^# - 1] &]] (* _Vladimir Joseph Stephan Orlovsky_, Jul 08 2011 *)

%t Accumulate@ MersennePrimeExponent@ Range@ 45 (* _Michael De Vlieger_, Jul 22 2018 *)

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

%K nonn

%O 1,1

%A _Jonathan Vos Post_, Aug 28 2005

%E a(38)-a(47) from _Gord Palameta_, Jul 21 2018