1,1

The known ratios of successive terms a(n)/a(n-1) are as follows. n a(n)/a(n-1) 2 120.70000... 3 121.18641... 4 101.30861... 5 102.87987... 6 101.16277... 7 100.73651... 8 100.85890... 9 100.59270... 10 100.45199... Heuristically, There appears to be a convergence. The PARI program computes the first 8 terms in a reasonable time. The 9th and 10th terms were computed by the program in the first link in 4,700 and 50,500 seconds respectively on a p4 2.53 ghz xp pro system.

Cino Hilliard, Program that can read a 115 gig file of the first 14.4 billion primes using win32api ReadFile().

Cino Hilliard, Power Basic program dll functions to read large files and some prime and twin prime routines.

For n=1 10^n = 10. The 10th prime is 29. The 4 twin prime pairs less than 29

are (3,5),(5,7),(11,13),(17,19). These add up to 80, which is the first term in

the sequence.

(PARI) sumtwins3(n) =\Using prime2() which reads primes2-370bill.bin using PB DLL { local(x, j, s, sr, p10x); sr=0; for(x=1, n, s=0; p10x = prime2(10^x); forstep(j=3, p10x, 2, if(ispseudoprime(j) & ispseudoprime(j+2) & j+2 <= p10x, s+=j+j+2); ); print1(s", "); sr+=1./s; ); print(); print(sr) } prime2(n) = \The n-th prime using prime.exe calling prime2-370bill.bin { local(x, s); s=concat("f:/sieve/prime ", Str(n)); s=concat(s, " > temp.txt"); \Must save to a temp file for output system(s); return(read("temp.txt")) }

Sequence in context: A116252 A159734 A091754 this_sequence A159377 A068273 A068285

Adjacent sequences: A118490 A118491 A118492 this_sequence A118494 A118495 A118496

hard,more,nonn

Cino Hilliard (hillcino368(AT)gmail.com), May 05 2006

a(11) from Giovanni Resta (g.resta(AT)iit.cnr.it), May 09 2006