A146536 - OEIS

%I #30 Jan 21 2024 20:33:29

%S 8,908,328184,69004076,11556327260,1707243198956,237064232862404,

%T 31153163750203064,3947120494191630260,486665774050923191336,

%U 58727077924563028184984

%N Sum of the first 10^n twin primes.

%C 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.

%H Cino Hilliard, <a href="http://groups.google.com/group/sumprimes/web/sumtwinsfirstn-c">Counting and summing primes</a> [Dead link]

%H Kevin Ryde, <a href="/A146536/a146536.c.txt">C Code</a>

%F a(n) = A086169(10^n). - _Andrew Howroyd_, Oct 22 2023

%e The 10^0-th twin prime pair is (3,5). This adds up to 8, the first entry in the sequence.

%e 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.

%o (C) // See links.

%o (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

%Y Cf. A086169, A118552.

%K nonn,more

%O 0,1

%A _Cino Hilliard_, Oct 31 2008

%E a(10) corrected by _Bill McEachen_, Oct 16 2023