%I
%S 1,3,2,6,13,5,19,7,43,11,33,61,17,45,79,23,125,29,67,31,157,37,129,41,
%T 91,147,47,215,53,233,59,123,259,203,71,143,73,301,235,83,329,89,433,
%U 97,277,101,195,103,299,107,209,109,321,113,883,127,355,131,485,137
%N a(1)=1. For n > 1, a(n) = the smallest positive integer not included earlier such that the nth partial sum is n times a prime.
%C Equivalently, for n > 1, a(n) is the smallest number not already in the sequence such that the arithmetic mean of the first n terms is prime.  _Derek Orr_, Jun 26 2015
%C Conjectured not to be a permutation of the natural numbers. The numbers that have not been used before the 2000th term: 4, 8, 9, 10, 12, 14, 15, 16, 18, 20, 22, ...  _Derek Orr_, Jun 26 2015
%H Derek Orr, <a href="/A073883/b073883.txt">Table of n, a(n) for n = 1..2000</a>
%o (PARI) v=[1]; n=1; while(#v<200, s=(n+vecsum(v))/(#v+1); if(type(s)=="t_INT", if(isprime(s)&&!vecsearch(vecsort(v), n), v=concat(v, n); n=0)); n++); v \\ _Derek Orr_, Jun 26 2015
%K nonn
%O 1,2
%A _Amarnath Murthy_, Aug 16 2002
%E Corrected and extended by _Sascha Kurz_, Feb 01 2003
