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A143293
Partial sums of A002110, the primorial numbers.
58
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)
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
KEYWORD
nonn
AUTHOR
Gary W. Adamson, Aug 05 2008
EXTENSIONS
a(11)-a(19) from Jonathan Vos Post, Feb 10 2010
STATUS
approved