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 A180101 #17 Mar 30 2012 16:51:57 %S A180101 0,1,1,2,2,3,3,3,5,5,5,5,7,7,7,7,7,7,11,11,11,11,11,11,13,13,13,13,13, %T A180101 13,17,17,17,17,17,17,19,19,19,19,19,19,23,23,23,23,23,23,23,23,23,23, %U A180101 29,29,29,29,29,29,29,29,31,31,31,31,31,31,31,31,37,37,37,37,37,37,37,37,37,37,41,41,41,41 %N A180101 a(0)=0, a(1)=1; thereafter a(n) = largest prime factor of sum of all previous terms. %C A180101 More precisely, a(n) = A006530 applied to sum of previous terms. %C A180101 Inspired by A175723. %C A180101 Except for initial terms, same as A076272, but the simple definition warrants an independent entry. %F A180101 For the purposes of this paragraph, regard 0 as the (-1)st prime and 1 as the 0th prime. Conjectures: All primes appear; the primes appear in increasing order; the k-th prime p(k) appears p(k+1)-p(k-1) times (cf. A031131); and p(k) appears for the first time at position A164653(k) (sums of two consecutive primes). These assertions are stated as conjectures only because I have not written out a formal proof, but they are surely true. %Y A180101 Cf. A006530, A076272, A175723, A180107 (partial sums). %K A180101 nonn %O A180101 0,4 %A A180101 _N. J. A. Sloane_, Jan 16 2011