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a(1)=2. a(n) is the a(n-1)st integer from among those positive integers coprime to a(n-1).
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%I #9 Oct 10 2019 13:39:40

%S 2,3,4,7,8,15,28,65,87,134,271,272,577,578,1227,1844,3695,4624,9825,

%T 18562,37127,37537,37538,75627,113480,283799,283800,1198543,1201967,

%U 1302144,3907583,3907584,11948189,13143019,13151298,39453911,46029570

%N a(1)=2. a(n) is the a(n-1)st integer from among those positive integers coprime to a(n-1).

%F a(n) = A069213(a(n-1)).

%e a(4)=7. So a(5) is the 7th positive integer which is coprime to 7. 7 is coprime to 1,2,3,4,5,6,8,9,10,... So a(5) is the 7th of these, which is 8.

%t f[n_] := Block[{k = 0, c = n},While[c > 0,k++;While[GCD[k, n] > 1, k++ ];c--;];k];g[l_] := Append[l, f[l[[ -1]]]];Nest[g, {2}, 36] (* _Ray Chandler_, Dec 31 2006 *)

%Y Cf. A069213, A126881.

%K nonn

%O 1,1

%A _Leroy Quet_, Dec 29 2006

%E Extended by _Ray Chandler_, Dec 31 2006