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%I #15 Dec 11 2019 21:33:43
%S 1,2,4,3,6,5,12,7,16,9,14,13,8,11,10,17,18,15,22,24,20,23,26,25,30,28,
%T 32,33,38,29,48,27,34,44,36,19,42,47,52,35,50,21,56,53,46,39,60,45,54,
%U 31,40,37,58,49,70,55,68,61,72,43,98,41,74,57,84,59,78,64,82
%N a(1) = 1; a(n) is the smallest positive integer not already in the sequence such that Sum_{k=1..n} k*a(k) is a prime.
%C Proposed by _Leroy Quet_, Feb 13 2004; computed by several people including Fred W. Helenius, Feb 14 2004.
%C Comment from Fred Helenius: Every positive integer up to 82 appears in the first 100 terms; everything up to 922 appears in the first 1000. Apart from a(1), odd-indexed terms must be even; even-indexed terms are occasionally even as well, so the odd values tend to arrive late.
%o (PARI) v=[1];n=1;while(n<100,s=n*(#v+1)+sum(i=1,#v,i*v[i]);if(isprime(s)&&!vecsearch(vecsort(v),n),v=concat(v,n);n=0);n++);v \\ _Derek Orr_, Jun 03 2015
%Y Cf. A091851.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_, Mar 13 2004