A143293 Partial sums of A002110, the primorial numbers.

1, 3, 9, 39, 249, 2559, 32589, 543099, 10242789, 233335659, 6703028889, 207263519019, 7628001653829, 311878265181039, 13394639596851069, 628284422185342479, 33217442899375387209, 1955977793053588026279, 119244359152460559009549, 7977565910232727614888639

Offset

0,2

Comments

After 3, this is never prime because all values thereafter are multiples of 3. Starting from a(6) all are also multiples of 17. - Jonathan Vos Post, Feb 10 2010

Starting from a(162) all are also multiples of 967. - Alex Ratushnyak, May 14 2013

Repunits in primorial base, A049345. - Antti Karttunen, Aug 21 2016

Links

Soumyadeep Dhar, Table of n, a(n) for n = 0..350 (terms up to a(100) from T. D. Noe)

Index entries for sequences related to primorial base

Formula

a(n) = Sum_{k=0..n} prime(k)#, where prime(n)# = A002110(n).

a(n) = A276085(A002110(1+n)). - Antti Karttunen, Aug 21 2016

Example

a(3) = 39 = (1 + 2 + 6 + 30), where A002110 = (1, 2, 6, 30, 210, 2310,...).

Maple

b:= proc(n) option remember; `if`(n=0, [1$2], (h->
      (p-> [p, p+h[2]])(ithprime(n)*h[1]))(b(n-1)))
    end:
a:= n-> b(n)[2]:
seq(a(n), n=0..19);  # Alois P. Heinz, Feb 23 2022

Mathematica

Table[s = 1; Do[s = 1 + s*Prime[i], {i, n, 1, -1}]; s, {n, 0, 20}] (* T. D. Noe, May 03 2013 *)
Accumulate[FoldList[Times, 1, Prime[Range[20]]]] (* Harvey P. Dale, Feb 05 2015 *)

Prog

(PARI) a(n)=if(n==0, return(1)); my(P=1, s=1); forprime(p=2, prime(n), s+=P*=p); s \\ Charles R Greathouse IV, Feb 05 2014
(Python)
from itertools import chain, accumulate, count, islice
from operator import mul
from sympy import prime
def A143293_gen(): # generator of terms
    return accumulate(accumulate(chain((1, ), (prime(n) for n in count(1))), mul))
A143293_list = list(islice(A143293_gen(), 20)) # Chai Wah Wu, Feb 23 2022

Crossrefs

Cf. A002110, A049345, A276085.

Sequence in context: A090012 A340913 A079096 * A101395 A365121 A229244

Adjacent sequences: A143290 A143291 A143292 * A143294 A143295 A143296

Keyword

nonn

Author

Gary W. Adamson, Aug 05 2008

Extensions

a(11)-a(19) from Jonathan Vos Post, Feb 10 2010

Status

approved