A356087 Intersection of A001952 and A054406.

23, 30, 37, 40, 44, 47, 54, 61, 68, 75, 78, 85, 92, 99, 139, 146, 153, 160, 163, 167, 170, 177, 184, 191, 194, 198, 201, 208, 215, 238, 262, 269, 276, 279, 283, 286, 288, 291, 293, 295, 298, 300, 302, 305, 307, 309, 312, 314, 317, 319, 321, 324, 326, 328

Offset: 1

Author

Clark Kimberling, Aug 04 2022

Keywords

• nonn
• easy

Comments

This is the fourth 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, ...) = A356085.
(3)  u' ^ v  = ( 3,  6, 10, 13, 17, 20, 27, 34, 51, 58, 64, 71, ...) = A356086.
(4)  u' ^ v' = (23, 30, 37, 40, 44, 47, 54, 61, 68, 75, 78, 85, ...) = A356087.
		

Crossrefs

Cf. A001951, A001952, A022838, A054406, A346308, A356085, A356086, A356088 (results of composition instead of intersections).

Programs

Mathematica

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 *)
Intersection[u, v]    (* A346308 *)
Intersection[u, v1]   (* A356085 *)
Intersection[u1, v]   (* A356086 *)
Intersection[u1, v1]  (* A356087 *)