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%I #5 Oct 01 2013 21:35:25
%S 37,3989,424372,44268603,4545653462,462450097976,46796680005643,
%T 4720790259612723,475260488407745464,47779177572418270761,
%U 4798532922306255318985,481564411447949294088622
%N Sum of the composite numbers <= 10^n.
%C Conjecture: 10^n(10^n+1)/2 - 1 -(10^n)^2/(2*log(10^n)-1) -> a(n) as n -> infinity. Here (10^n)^2/(2*log(10^n)-1) is also conjectured to -> sum of primes < 10^n and is a very good approximation for the sum of primes < 10^n. We know that k^2/(2log(k)-1) diverges as k -> infinity. So if we can prove this limit approaches the sum of the primes <= k, then this implies the sum of primes is infinite and therefore the number of primes is infinite.
%F 10^n(10^n+1)/2 - 1 - A046731(n). Note: The b-file from Marc Deleglise was used for A046731(16) to A046731(20).
%e The sum of the composite numbers <= 10^1 is 4+6+8+9+10 = 37, the first entry in the sequence.
%Y Cf. A046731.
%K nonn
%O 1,1
%A _Cino Hilliard_, Jun 01 2008
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