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

1,2

Links

Table of n, a(n) for n=1..60.

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

Adjacent sequences: A076916 A076917 A076918 * A076920 A076921 A076922

Keyword

nonn

Author

Amarnath Murthy, Oct 17 2002

Extensions

More terms from Jean-François Alcover, Oct 25 2023

Status

approved