1,1

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 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). Eg., Sum of twin primes <= 10^8 divided by 4 = 10301443659233. Pi_2(10^16) = 10304185697298. This is an error of .00002661.

Cino Hilliard, Sum of twin primes less than 10^n.

Pi_2(n): Number of twin prime pairs <= n.

(3,5),(5,7) are the two twin prime pairs less than 10. These add up to 20, the

first term in the sequence.

(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", "); ) }

Sequence in context: A065412 A159753 A000827 this_sequence A092087 A008270 A130186

Adjacent sequences: A118549 A118550 A118551 this_sequence A118553 A118554 A118555

hard,nonn

Cino Hilliard (hillcino368(AT)gmail.com), May 07 2006

2 more terms from Giovanni Resta (g.resta(AT)iit.cnr.it), May 08 2006

Added a(13) and a(14).Added to the comment. Changed the link to a better program.Edited the example. - Cino Hilliard (hillcino368(AT)hotmail.com), Nov 18 2008