A356105 a(n) = A000201(A108598(n)).

1, 4, 8, 11, 14, 16, 19, 22, 25, 29, 30, 33, 37, 40, 43, 45, 48, 51, 55, 58, 59, 63, 66, 69, 72, 76, 77, 80, 84, 87, 90, 92, 95, 98, 101, 105, 106, 110, 113, 116, 119, 121, 124, 127, 131, 134, 137, 139, 142, 145, 148, 152, 153, 156, 160, 163, 166, 168, 171

Offset: 1

Author

Clark Kimberling, Sep 08 2022

Keywords

• nonn
• easy

Comments

This is the second of four sequences that partition the positive integers. See A356104.

Examples

			(1)  u o v = (3, 6, 9, 12, 17, 21, 24, 27, 32, 35, 38, 42, 46, ...) = A356104
(2)  u o v' = (1, 4, 8, 11, 14, 16, 19, 22, 25, 29, 30, 33, 37, ...) = A356105
(3)  u' o v = (5, 10, 15, 20, 28, 34, 39, 44, 52, 57, 62, 68, ...) = A356106
(4)  u' o v' = (2, 7, 13, 18, 23, 26, 31, 36, 41, 47, 49, 54, ...) = A356107
		

Crossrefs

Cf. u = A000201, u' = A001950, v = A022839, v' = A108598, A356104, A356106, A356107, A351415 (intersections), A356217 (reverse composites).

Programs

Mathematica

z = 1000;
u = Table[Floor[n*(1 + Sqrt[5])/2], {n, 1, z}];  (* A000201 *)
u1 = Complement[Range[Max[u]], u];  (* A001950 *)
v = Table[Floor[n*Sqrt[5]], {n, 1, z}];  (* A022839 *)
v1 = Complement[Range[Max[v]], v];  (* A108598 *)
zz = 120;
Table[u[[v[[n]]]], {n, 1, zz}]    (* A356104 *)
Table[u[[v1[[n]]]], {n, 1, zz}]   (* A356105 *)
Table[u1[[v[[n]]]], {n, 1, zz}]   (* A356106 *)
Table[u1[[v1[[n]]]], {n, 1, zz}]  (* A356107 *)