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A076919 a(1) = 1, a(2) = 2, then a(n+1) is the smallest number such that the highest common factor of a(n) and a(n+1) is different from that of a(n) and a(n-1) and is more than 1.

%I A076919 #5 Oct 25 2023 07:38:03
%S A076919 1,2,4,8,10,15,18,20,24,26,39,42,44,48,50,55,66,68,72,74,111,114,116,
%T A076919 120,122,183,186,188,192,194,291,294,296,300,302,453,456,458,687,690,
%U A076919 692,696,698,1047,1050,1052,1056,1058,1081,1128,1130,1135,1362,1364,1368,1370,1375,1386,1388,1392
%N A076919 a(1) = 1, a(2) = 2, then a(n+1) is the smallest number such that the highest common factor of a(n) and a(n+1) is different from that of a(n) and a(n-1) and is more than 1.
%e A076919 15 follows 10 as (8,10) = 2 so 12 and 14 are ruled out.
%t A076919 a[1] = 1; a[2] = 2;
%t A076919 a[n_] := a[n] = Module[{k}, For[k = a[n-1] + 1, True, k++, If[GCD[a[n-1], a[n-2]] != GCD[k, a[n-1]] && GCD[k, a[n-1]] > 1, Return[k]]]];
%t A076919 Table[a[n], {n, 1, 60}] (* _Jean-François Alcover_, Oct 25 2023 *)
%Y A076919 Cf. A076920.
%K A076919 nonn
%O A076919 1,2
%A A076919 _Amarnath Murthy_, Oct 17 2002
%E A076919 More terms from _Jean-François Alcover_, Oct 25 2023