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A143293 Partial sums of A002110, the primorial numbers. 15

%I

%S 1,3,9,39,249,2559,32589,543099,10242789,233335659,6703028889,

%T 207263519019,7628001653829,311878265181039,13394639596851069,

%U 628284422185342479,33217442899375387209,1955977793053588026279,119244359152460559009549

%N Partial sums of A002110, the primorial numbers.

%C 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

%C Starting from a(162) all are also multiples of 967. - _Alex Ratushnyak_, May 14 2013

%C Repunits in primorial base, A049345. - _Antti Karttunen_, Aug 21 2016

%H T. D. Noe, <a href="/A143293/b143293.txt">Table of n, a(n) for n = 0..100</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

%F a(n) = Sum__{0..n} prime(n)#, where prime(n)# = A002110(n).

%F a(n) = A276085(A002110(1+n)). - _Antti Karttunen_, Aug 21 2016

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

%t Table[s = 1; Do[s = 1 + s*Prime[i], {i, n, 1, -1}]; s, {n, 0, 20}] (* _T. D. Noe_, May 03 2013 *)

%t Accumulate[FoldList[Times,1,Prime[Range[20]]]] (* _Harvey P. Dale_, Feb 05 2015 *)

%o (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

%Y Cf. A002110, A049345, A276085.

%K nonn

%O 0,2

%A _Gary W. Adamson_, Aug 05 2008

%E a(11)-a(19) from _Jonathan Vos Post_, Feb 10 2010

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Last modified March 21 07:23 EDT 2019. Contains 321367 sequences. (Running on oeis4.)