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A164912 Dual EKG: a(n) = A008619(A064413(n) - 1).

%I A164912 #31 Nov 24 2021 03:04:58
%S A164912 1,1,2,3,2,5,6,4,5,3,8,9,7,4,11,12,8,10,11,6,17,14,15,13,18,14,13,7,
%T A164912 20,18,16,17,9,26,21,19,10,29,23,20,22,23,12,35,24,25,26,27,28,25,32,
%U A164912 30,28,33,35,29,15,44,33,31,16,47,36,32,34,37,19,56
%N A164912 Dual EKG: a(n) = A008619(A064413(n) - 1).
%C A164912 First occurrences of n have ranks: 1, 3, 4, 8, 6, 7, 13, 11, 12, 18, ...
%C A164912 Second occurrences of n have ranks: 2, 5, 10, 14, 9, 20, ...
%C A164912 Triples of the form (a, b, a+b): (1,1,2), (3,2,5), (5,3,8), (7,4,11), (11,6,17), ... give sequence 2, 5, 8, 11, 17, ....
%C A164912 Every positive integer appears exactly twice. - _Charlie Neder_, Jan 12 2019
%H A164912 Michael De Vlieger, <a href="/A164912/b164912.txt">Table of n, a(n) for n = 1..10000</a>
%F A164912 a(n) = A008619(A064413(n)-1) = ceiling(A064413(n)/2). - _Charlie Neder_, Jan 12 2019
%t A164912 ekg[n_] := ekg[n] = Module[{ee, k},
%t A164912      If[n <= 2, n, ee = Array[ekg, n - 1];
%t A164912      For[k = 1, True, k++, If[FreeQ[ee, k] &&
%t A164912      GCD[ekg[n - 1], k] != 1, Return[k]]]]];
%t A164912 a[n_] := Quotient[ekg[n] - 1, 2] + 1;
%t A164912 Array[a, 68] (* _Jean-François Alcover_, Nov 21 2021 *)
%Y A164912 Cf. A000027, A008619, A064413.
%K A164912 nonn
%O A164912 1,3
%A A164912 _Paul Curtz_, Aug 31 2009
%E A164912 More terms from _Charlie Neder_, Jan 12 2019
%E A164912 Name modified by _Jean-François Alcover_, Nov 23 2021