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.

1, 2, 4, 8, 10, 15, 18, 20, 24, 26, 39, 42, 44, 48, 50, 55, 66, 68, 72, 74, 111, 114, 116, 120, 122, 183, 186, 188, 192, 194, 291, 294, 296, 300, 302, 453, 456, 458, 687, 690, 692, 696, 698, 1047, 1050, 1052, 1056, 1058, 1081, 1128, 1130, 1135, 1362, 1364, 1368, 1370, 1375, 1386, 1388, 1392

Offset: 1

Author

Amarnath Murthy, Oct 17 2002

Keywords

• nonn

Examples

			15 follows 10 as (8,10) = 2 so 12 and 14 are ruled out.
		

Crossrefs

Cf. A076920.

Programs

Mathematica

a[1] = 1; a[2] = 2;
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]]]];
Table[a[n], {n, 1, 60}] (* Jean-François Alcover, Oct 25 2023 *)

Extensions

More terms from Jean-François Alcover, Oct 25 2023