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A076560 a(1)=1; a(n>1)= greatest prime divisor of (a(n-1) + n).

%I A076560 #12 Jun 21 2023 04:02:01
%S A076560 1,3,3,7,3,3,5,13,11,7,3,5,3,17,2,3,5,23,7,3,3,5,7,31,7,11,19,47,19,7,
%T A076560 19,17,5,13,3,13,5,43,41,3,11,53,3,47,23,23,7,11,5,11,31,83,17,71,7,7,
%U A076560 2,5,2,31,23,17,5,23,11,11,13,3,3,73,3,5,13,29,13,89,83,23,17,97,89,19
%N A076560 a(1)=1; a(n>1)= greatest prime divisor of (a(n-1) + n).
%H A076560 Harvey P. Dale, <a href="/A076560/b076560.txt">Table of n, a(n) for n = 1..1000</a>
%t A076560 nxt[{n_,a_}]:={n+1,FactorInteger[a+n+1][[-1,1]]}; Transpose[NestList[nxt,{1,1},90]][[2]] (* _Harvey P. Dale_, Nov 29 2013 *)
%o A076560 (PARI) gpf(n) = if(n==1,1, my(v=factor(n)[,1]); v[#v]);
%o A076560 a_vector(len) = my(t=0); vector(len,n, t=gpf(t+n)); \\ _Kevin Ryde_, Jun 21 2023
%Y A076560 Cf. A006530 (gpf), A362138.
%K A076560 easy,nonn
%O A076560 1,2
%A A076560 _Zak Seidov_, Oct 19 2002
%E A076560 Definition clarified by _Harvey P. Dale_, Nov 29 2013