A356085 Intersection of A001951 and A054406.

2, 4, 7, 9, 11, 14, 16, 18, 21, 26, 28, 33, 35, 42, 49, 52, 56, 59, 63, 66, 70, 73, 80, 82, 87, 89, 94, 97, 101, 104, 106, 108, 111, 113, 115, 118, 120, 123, 125, 127, 130, 132, 134, 137, 141, 144, 149, 151, 156, 158, 165, 172, 175, 179, 182, 186, 189, 196

Offset: 1

Author

Clark Kimberling, Jul 26 2022

Keywords

• nonn
• easy

Comments

This is the second of four sequences, u^v, u^v', u'^v, u'^v', that partition the positive integers. See A346308.

Examples

			(1)  u ^ v = (1, 5, 8, 12, 15, 19, 22, 24, 25, 29, 31, 32, ...) =  A346308
(2)  u ^ v' = (2, 4, 7, 9, 11, 14, 16, 18, 21, 26, 28, 33, 35, ...) =  A356085
(3)  u' ^ v = (3, 6, 10, 13, 17, 20, 27, 34, 51, 58, 64, 71, 81, ...) = A356086
(4)  u' ^ v' = (23, 30, 37, 40, 44, 47, 54, 61, 68, 75, 78, 85, ...) = A356087
		

Crossrefs

Cf. A001951, A001952, A022838, A054406, A346308, A356086, A356087, A356088 (composites instead of intersections).

Programs

Mathematica

z = 200;
r = Sqrt[2]; u = Table[Floor[n*r], {n, 1, z}]  (* A001951 *)
u1 = Take[Complement[Range[1000], u], z]  (* A001952 *)
r1 = Sqrt[3]; v = Table[Floor[n*r1], {n, 1, z}]  (* A022838 *)
v1 = Take[Complement[Range[1000], v], z]  (* A054406 *)
t1 = Intersection[u, v]    (* A346308 *)
t2 = Intersection[u, v1]   (* A356085 *)
t3 = Intersection[u1, v]   (* A356086 *)
t4 = Intersection[u1, v1]  (* A356087 *)