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%I #12 Mar 01 2016 06:22:51
%S 0,1,2,5,3,11,5,7,19,5,29,7,43,31,7,5,17,13,43,11,13,37,29,19,67,17,
%T 101,73,19,37,31,11,53,13,79,19,13,5,23,17,19,11,41,31,103,79,29,137,
%U 101,113,109,331,257,13,283,193,223,71,73,31,5,41,29,11,17,5,3,11,5,7,19,5,29,7,43,31,7,5,17
%N a(0)=0, a(1)=1; thereafter a(n) = gpf(2*a(n-1)+a(n-2)), where gpf = "greatest prime factor" (A006530).
%C Rapidly enters a loop of length 62: [5, 3, 11, 5, 7, 19, 5, 29, 7, 43, 31, 7, 5, 17, 13, 43, 11, 13, 37, 29, 19, 67, 17, 101, 73, 19, 37, 31, 11, 53, 13, 79, 19, 13, 5, 23, 17, 19, 11, 41, 31, 103, 79, 29, 137, 101, 113, 109, 331, 257, 13, 283, 193, 223, 71, 73, 31, 5, 41, 29, 11, 17].
%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. [Discusses similar sequences]
%o (PARI) gpf(n) = if (n==1, 1, vecmax(factor(n)[,1]));
%o lista(nn) = {print1(x=0, ", "); print1(y=1, ", "); for (n=2, nn, z = gpf(x+2*y); print1(z, ", "); x = y; y = z;);} \\ _Michel Marcus_, Mar 01 2016
%Y Cf. A006530, A175723.
%K nonn
%O 0,3
%A _Gary W. Adamson_ and _N. J. A. Sloane_, Jan 19 2013
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