A114410 Cumulative sum of double primorials (A079078).

1, 3, 6, 16, 37, 147, 420, 2290, 7477, 50487, 200910, 1534220, 7099871, 61765581, 301088574, 2870376944, 15554495573, 167142509403, 940873745772, 11097270672382, 66032188454581, 807449164097111, 5147307668890832

Offset

0,2

Comments

The cumulative sum is prime for a(2) = 3, a(4) = 37, a(8) = 7477, a(12) = 7099871, a(16) = 15554495573. The sum a(n) is semiprime for n = 2, 9.

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = 0## + 1## + ... + n##, where n## = p(n)*(n-2)##, where p(n) is the n-th prime.

Example

n 0## + ... + n##
0 1.
1 1+2 = 3.
2 1+2+3 = 6.
3 1+2+3+10 = 16.
4 1+2+3+10+21 = 37.
5 1+2+3+10+21+110 = 147.
6 1+2+3+10+21+110+273 = 420.
7 1+2+3+10+21+110+273+1870 = 2290.
8 1+2+3+10+21+110+273+1870+5187 = 7477.
9 1+2+3+10+21+110+273+1870+5187+ 43010 = 50487.
10 1+2+3+10+21+110+273+1870+5187+ 43010 + 150423 = 200910.

Mathematica

p[0]=1; p[1]=2; p[n_] := p[n] = Prime[n]*p[n - 2]; Accumulate[p /@ Range[0, 22]] (* Giovanni Resta, Jun 14 2016 *)

Crossrefs

Cf. A079078.

Sequence in context: A203068 A362145 A321229 * A190735 A096588 A256943

Adjacent sequences: A114407 A114408 A114409 * A114411 A114412 A114413

Keyword

easy,nonn

Author

Jonathan Vos Post, Feb 12 2006

Extensions

Data corrected by Giovanni Resta, Jun 14 2016

Status

approved