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 A118552 #22 Oct 24 2024 23:52:33
%S A118552 20,488,24236,1726412,109114568,7424366648,545678596592,
%T A118552 41205774636932,3234489739234676,260643410442091112,
%U A118552 21446976192435396140,1795640886305783918948,152542601906447626814216,13119246582832293524505360
%N A118552 Sum of the twin prime pairs less than 10^n.
%C A118552 The PARI program can compute the first 9 terms in reasonable time. a(10) was computed by the program in the link. This took 145 sec on a p4 2.53 GHz processor while a(13) took 1.4 days and a(14) took 15 days with multitasking. The sum of twin primes < 10^n divided by 4 gives a very good approximation for the number of twin primes < 10^(2n). E.g., sum of twin primes <= 10^8 divided by 4 = 10301443659233. Pi_2(10^16) = 10304185697298. This is an error of 0.00002661. Pi_2(n): Number of twin prime pairs <= n.
%H A118552 Cino Hilliard, <a href="http://groups.google.com/group/sumprimes/web/sum-of-twin-primes--n">Sum of twin primes less than 10^n</a>. [Broken link]
%e A118552 (3,5),(5,7) are the two twin prime pairs less than 10. These add up to 20, the first term in the sequence.
%o A118552 (PARI) sumtwins(n) = { local(x,j,s,sr,p10x); for(x=1,n, s=0; p10x=10^x; forstep(j=3,10^x,2, if(j+2 < p10x && ispseudoprime(j) && ispseudoprime(j+2),s+=j+j+2); ); print1(s","); ) }
%Y A118552 Cf. A007508.
%K A118552 hard,nonn
%O A118552 1,1
%A A118552 _Cino Hilliard_, May 07 2006
%E A118552 2 more terms from _Giovanni Resta_, May 08 2006
%E A118552 a(13) and a(14) added, comment expanded, program at link improved, and example edited by _Cino Hilliard_, Nov 18 2008