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A060389 a(1)=p_1, a(2)=p_1 + p_1*p_2, a(3)=p_1 + p_1*p_2 + p_1*p_2*p_3, ... where p_i is the i-th prime.

%I A060389 #42 Jul 02 2025 16:02:01
%S A060389 2,8,38,248,2558,32588,543098,10242788,233335658,6703028888,
%T A060389 207263519018,7628001653828,311878265181038,13394639596851068,
%U A060389 628284422185342478,33217442899375387208,1955977793053588026278
%N A060389 a(1)=p_1, a(2)=p_1 + p_1*p_2, a(3)=p_1 + p_1*p_2 + p_1*p_2*p_3, ... where p_i is the i-th prime.
%C A060389 Partial sums of the primorials A002110 starting from 2. - _Charles R Greathouse IV_, Feb 05 2014
%C A060389 All terms are even. From a(98) on, all terms are multiples of 523. - _Charles R Greathouse IV_, Feb 05 2014
%C A060389 The only values of n for which a(n)/2 is prime are: 3, 5, 7, 11, 15, 47, 49. The corresponding 7 primes are: 19, 1279, 271549, 103631759509, 314142211092671239, 826811434211869939736645732264127163964562391958563586838409421490271014424018927729, 41839936239750050346953677118447851613901200239299781782205558511980130628486398081201749. - _Amiram Eldar_, May 04 2017
%H A060389 Vincenzo Librandi, <a href="/A060389/b060389.txt">Table of n, a(n) for n = 1..200</a>
%H A060389 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%F A060389 a(n) = A002110(n-2)*A286624(n-1) + a(n-3), n >= 4. - _Bob Selcoe_, Oct 12 2017
%F A060389 a(n) = A276085(A070826(1+n)) = A084737(2+n)-2 = A373158(A002110(n)). - _Antti Karttunen_, Feb 06 2024, Oct 28 2024
%e A060389 a(4) = 248 because p_1 + p_1*p_2 + p_1*p_2*p_3 + p_1*p_2*p_3*p_4 = 2 + 6 + 30 + 210 = 248.
%e A060389 a(5) = 2558: A002110(3) = 30, A286624(4) = 85, a(2) = 8; 30*85 + 8 = 2558. - _Bob Selcoe_, Oct 12 2017
%p A060389 for n from 1 to 30 do printf(`%d,`,sum(product(ithprime(i), i=1..j), j=1..n)) od:
%t A060389 Accumulate[Denominator[Accumulate[1/Prime[Range[20]]]]] (* _Alonso del Arte_, Mar 21 2013 *)
%t A060389 Accumulate@ FoldList[Times, Prime@ Range@ 17] (* _Michael De Vlieger_, May 04 2017 *)
%o A060389 (PARI) a(n)=my(s,P=1); forprime(p=2,prime(n),s+=P*=p); s \\ _Charles R Greathouse IV_, Feb 05 2014
%Y A060389 Cf. A002110, A070826, A084737, A143293, A203008 [= A327860(a(n))], A276085, A286624, A373158.
%K A060389 nonn
%O A060389 1,1
%A A060389 _Jason Earls_, Apr 04 2001
%E A060389 More terms from _James Sellers_, Apr 05 2001