This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A139043 #15 Jun 30 2024 03:30:59 %S A139043 37,3989,424372,44268603,4545653462,462450097976,46796680005643, %T A139043 4720790259612723,475260488407745464,47779177572418270761, %U A139043 4798532922306255318985,481564411447949294088622,48300753556627220581110505,4842410739289313059458438978,485307601483092493601774297633 %N A139043 Sum of the composite numbers <= 10^n. %C A139043 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. %H A139043 Amiram Eldar, <a href="/A139043/b139043.txt">Table of n, a(n) for n = 1..26</a> (calculated using the b-file at A046731) %F A139043 a(n) = 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 A139043 The sum of the composite numbers <= 10^1 is 4 + 6 + 8 + 9 + 10 = 37, the first entry in the sequence. %Y A139043 Cf. A046731. %K A139043 nonn %O A139043 1,1 %A A139043 _Cino Hilliard_, Jun 01 2008 %E A139043 a(13)-a(15) from _Amiram Eldar_, Jun 30 2024