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A143293 Partial sums of A002110, the primorial numbers. 15
1, 3, 9, 39, 249, 2559, 32589, 543099, 10242789, 233335659, 6703028889, 207263519019, 7628001653829, 311878265181039, 13394639596851069, 628284422185342479, 33217442899375387209, 1955977793053588026279, 119244359152460559009549 (list; graph; refs; listen; history; text; internal format)
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

T. D. Noe, Table of n, a(n) for n = 0..100

Index entries for sequences related to primorial base

FORMULA

a(n) = Sum__{0..n} prime(n)#, 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,...).

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

CROSSREFS

Cf. A002110, A049345, A276085.

Sequence in context: A058105 A090012 A079096 * A101395 A229244 A218504

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

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Last modified February 19 12:09 EST 2019. Contains 320310 sequences. (Running on oeis4.)