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%I #20 Mar 01 2016 06:23:23
%S 1,1,1,1,2,5,3,11,7,13,17,3,5,19,11,19,3,13,23,29,17,41,11,7,19,13,5,
%T 11,3,2,7,23,7,13,5,3,7,7,11,7,2,3,23,7,7,5,7,13,2,3,5,23,11,7,23,2,
%U 43,5,73,41,3,61,89,97,5,7,11,5,7,5,7,3,11,13,17,11,13,3,11,19,23,7,5,3,19,17,11,5,13,23,13,3,13,13,7,3,3,13,13,2,31,59,7,11,3,5,13,2,23,43,3,71,7,31
%N a(1)=a(2)=a(3)=a(4)=1; thereafter a(n) = gpf(a(n-1)+a(n-2)+a(n-3)+a(n-4)), where gpf is the greatest prime factor.
%C After 133 steps, enters a cycle of length 14.
%H Greg Back and Mihai Caragiu, <a href="http://www.fq.math.ca/Papers1/48-4/Back_Caragiu.pdf">The Greatest Prime Factor and Recurrent Sequences</a>, Fibonacci Quart. 48 (2010), no. 4, 358-362.
%t nxt[{a_,b_,c_,d_}]:={b,c,d,FactorInteger[a+b+c+d][[-1,1]]}; Transpose[ NestList[ nxt,{1,1,1,1},120]][[1]] (* _Harvey P. Dale_, Sep 24 2013 *)
%Y Cf. A006530, A175723, A177904.
%K nonn,easy
%O 1,5
%A _N. J. A. Sloane_, Dec 18 2010
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