This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A114410 #6 Jun 15 2016 08:59:58 %S A114410 1,3,6,16,37,147,420,2290,7477,50487,200910,1534220,7099871,61765581, %T A114410 301088574,2870376944,15554495573,167142509403,940873745772, %U A114410 11097270672382,66032188454581,807449164097111,5147307668890832 %N A114410 Cumulative sum of double primorials (A079078). %C A114410 The cumulative sum is prime for a(2) = 3, a(4) = 37, a(8) = 7477, a(12) = 7099871, a(16) = 15554495573. The sum a(n) is semiprime for n = 2, 9. %F A114410 a(n) = 0## + 1## + ... + n##, where n## = p(n)*(n-2)##, where p(n) is the n-th prime. %e A114410 n 0## + ... + n## %e A114410 0 1. %e A114410 1 1+2 = 3. %e A114410 2 1+2+3 = 6. %e A114410 3 1+2+3+10 = 16. %e A114410 4 1+2+3+10+21 = 37. %e A114410 5 1+2+3+10+21+110 = 147. %e A114410 6 1+2+3+10+21+110+273 = 420. %e A114410 7 1+2+3+10+21+110+273+1870 = 2290. %e A114410 8 1+2+3+10+21+110+273+1870+5187 = 7477. %e A114410 9 1+2+3+10+21+110+273+1870+5187+ 43010 = 50487. %e A114410 10 1+2+3+10+21+110+273+1870+5187+ 43010 + 150423 = 200910. %t A114410 p[0]=1; p[1]=2; p[n_] := p[n] = Prime[n]*p[n - 2]; Accumulate[p /@ Range[0, 22]] (* _Giovanni Resta_, Jun 14 2016 *) %Y A114410 Cf. A079078. %K A114410 easy,nonn %O A114410 0,2 %A A114410 _Jonathan Vos Post_, Feb 12 2006 %E A114410 Data corrected by _Giovanni Resta_, Jun 14 2016