

A109472


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


2



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
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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

Gord Palameta, Table of n, a(n) for n = 1..47


FORMULA

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


EXAMPLE

a(1) = 2, since 2^21 = 3 is a Mersenne prime.
a(2) = 2 + 3 = 5, since 2^31 = 7 is a Mersenne prime.
a(3) = 2 + 3 + 5 = 10, since 2^51 = 31 is a Mersenne prime.
a(4) = 2 + 3 + 5 + 7 = 17, since 2^71 = 127 is a Mersenne prime; 17 itself is prime (in fact a p such that 2^p1 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, A057951A057958.
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



