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a(0) = 1. a(n) = the n-th integer from among those positive integers coprime to a(n-1).
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%I #10 Oct 11 2019 12:33:45

%S 1,1,2,5,4,9,8,13,8,17,10,27,17,13,15,28,37,17,19,20,49,24,65,31,24,

%T 73,26,57,44,63,52,67,32,65,46,73,36,109,38,81,59,41,43,44,95,59,46,

%U 97,48,145,64,101,52,113,54,163,56,131,58,121,65,82,127,63,110,177,100,167,68

%N a(0) = 1. a(n) = the n-th integer from among those positive integers coprime to a(n-1).

%e The positive integers coprime to a(6)=8 are 1,3,5,7,9,11,13,15,17,19... The seventh of these is 13, so a(7) = 13.

%t f[l_List] := Block[{k = 0, c = Length[l]},While[c > 0,k++;While[ GCD[k, l[[ -1]]] > 1, k++ ];c--;];Append[l, k]];Nest[f, {1}, 70] (* _Ray Chandler_, Nov 11 2006 *)

%K nonn

%O 0,3

%A _Leroy Quet_, Nov 08 2006

%E Extended by _Ray Chandler_, Nov 11 2006