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a(1)=a(2)=1; thereafter a(n) = lpf(a(n-1)+a(n-2)), where lpf = "least prime factor".
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%I #13 May 29 2023 11:46:59

%S 1,1,2,3,5,2,7,3,2,5,7,2,3,5,2,7,3,2,5,7,2,3,5,2,7,3,2,5,7,2,3,5,2,7,

%T 3,2,5,7,2,3,5,2,7,3,2,5,7,2,3,5,2,7,3,2,5,7,2,3,5,2,7,3,2,5,7,2,3,5,

%U 2,7,3,2,5,7,2,3,5,2,7,3,2,5,7,2,3,5,2,7,3,2,5,7,2,3,5,2,7,3,2,5,7,2,3,5,2,7,3,2,5,7

%N a(1)=a(2)=1; thereafter a(n) = lpf(a(n-1)+a(n-2)), where lpf = "least prime factor".

%C Cycles with a period of length 9.

%t nxt[{a_,b_}]:={b,FactorInteger[a+b][[1,1]]}; NestList[nxt,{1,1},110][[;;,1]] (* or *) PadRight[ {1,1},110,{5,7,2,3,5,2,7,3,2}] (* _Harvey P. Dale_, May 29 2023 *)

%Y Cf. A000045, A175723, A020639, A178095.

%K nonn

%O 1,3

%A _N. J. A. Sloane_, Dec 16 2010