%I #16 Nov 23 2018 03:16:26
%S 2,2,2,3,3,3,5,5,5,5,7,7,7,7,7,7,11,11,11,11,11,11,13,13,13,13,13,13,
%T 17,17,17,17,17,17,19,19,19,19,19,19,23,23,23,23,23,23,23,23,23,23,29,
%U 29,29,29,29,29,29,29,31,31,31,31,31,31,31,31,37,37,37,37,37,37,37,37
%N Starting with 2, largest prime divisor of the sum of all previous terms.
%C Conjecture: start from any initial value a(1) = m >= 2 and define a(n) to be the largest prime factor of a(1)+a(2)+...+a(n-1); then a(n) = n/2 + O(log(n)) and there are infinitely many primes p such that a(2p)=p. - _Benoit Cloitre_, Jun 04 2003
%H Harvey P. Dale, <a href="/A076973/b076973.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = p(m) (the m-th prime), where m is the smallest index such that n <= p(m+1) + p(m) - 2. - _Max Alekseyev_, Oct 21 2008
%t nxt[{t_,a_}]:=Module[{c=FactorInteger[t][[-1,1]]},{t+c,c}]; NestList[nxt,{2,2},80][[All,2]] (* _Harvey P. Dale_, May 21 2017 *)
%Y From the third term onwards the sequence coincides with A076272.
%K nonn
%O 1,1
%A _Amarnath Murthy_, Oct 22 2002
%E More terms from _Sascha Kurz_, Jan 22 2003
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