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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.
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
1,2
EXAMPLE
15 follows 10 as (8,10) = 2 so 12 and 14 are ruled out.
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 *)
CROSSREFS
Cf. A076920.
Sequence in context: A323102 A331627 A102431 * A336659 A341655 A171757
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Oct 17 2002
EXTENSIONS
More terms from Jean-François Alcover, Oct 25 2023
STATUS
approved