login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A114410 Cumulative sum of double primorials (A079078). 1
1, 3, 6, 16, 37, 147, 420, 2290, 7477, 50487, 200910, 1534220, 7099871, 61765581, 301088574, 2870376944, 15554495573, 167142509403, 940873745772, 11097270672382, 66032188454581, 807449164097111, 5147307668890832 (list; graph; refs; listen; history; text; internal format)
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: A027852 A203068 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 3 01:56 EDT 2022. Contains 355029 sequences. (Running on oeis4.)