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A118493
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Sum of the components of twin prime pairs less than the 10^n-th prime.
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0
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80, 9656, 1170176, 118548908, 12196296524, 1233811181036, 124289829648164, 12535736299783460, 1261003658138370872, 126670338265079023748, 12714730302282303009284
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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PROG
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(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")) }
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CROSSREFS
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KEYWORD
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hard,more,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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