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A146536
Sum of the first 10^n twin primes.
1
8, 908, 328184, 69004076, 11556327260, 1707243198956, 237064232862404, 31153163750203064, 3947120494191630260, 486665774050923191336, 58727077924563028184984
OFFSET
0,1
COMMENTS
The author's Gcc/Gmp program is in the links section. The page also has the PARI bisection algorithms which give a very good approximation for the n-th prime number and the n-th lower twin prime number. The first 5 terms can be computed from the PARI script although 11556327260 takes 4 hours on a 2.53ghz 2 gig ram p4.
LINKS
Cino Hilliard, Counting and summing primes [Dead link]
Kevin Ryde, C Code
FORMULA
a(n) = A086169(10^n). - Andrew Howroyd, Oct 22 2023
EXAMPLE
The 10^0-th twin prime pair is (3,5). This adds up to 8, the first entry in the sequence.
The first 10^1 twin prime pairs are (3,5),(5,7),(11,13) (17,19),(29,31),(41,43),(59,61),(71,73),(101,103),(107,109). This adds up to 908, the second entry in the table.
PROG
(C) // See links.
(PARI) a(n)={my(k=10^n, s=k, q); forprime(p=3, oo, if(p==q+2, s+=q; k--; if(!k, return(2*s))); q=p)} \\ Andrew Howroyd, Oct 22 2023
CROSSREFS
Sequence in context: A112578 A112579 A064072 * A189646 A348795 A304018
KEYWORD
nonn,more
AUTHOR
Cino Hilliard, Oct 31 2008
EXTENSIONS
a(10) corrected by Bill McEachen, Oct 16 2023
STATUS
approved