A356054 Intersection of A001952 and A137803.

3, 13, 17, 30, 34, 40, 44, 47, 51, 61, 68, 78, 88, 95, 99, 105, 109, 112, 116, 122, 126, 133, 139, 143, 153, 160, 170, 174, 187, 191, 204, 208, 218, 225, 235, 245, 252, 256, 262, 266, 269, 273, 279, 283, 290, 300, 310, 317, 327, 331, 334, 338, 344, 348

Offset: 1

Author

Clark Kimberling, Jul 26 2022

Keywords

• nonn
• easy

Comments

This is the third of four sequences, u^v, u^v', u'^v, u'^v', that partition the positive integers. See A356052.

Examples

			(1)  u ^ v = (1, 5, 7, 9, 11, 15, 19, 21, 22, 24, 26, 28, ...) =  A356052
(2)  u ^ v' = (2, 4, 8, 12, 14, 16, 18, 25, 29, 31, 33, 35, ...) =  A356053
(3)  u' ^ v = (3, 13, 17, 30, 34, 40, 44, 47, 51, 61, 68, ...) = A356054
(4)  u' ^ v' = (6, 10, 20, 23, 27, 37, 54, 58, 64, 71, 75, ...) = A356055
		

Crossrefs

Cf. A001951, A001952, A136803, A137804, A356052, A356054, A356055, A356056 (composites instead of intersections).

Programs

Mathematica

z = 250;
u = Table[Floor[n (Sqrt[2])], {n, 1, z}]   (* A001951 *)
u1 = Complement[Range[Max[u]], u]     (* A001952 *)
v = Table[Floor[n (1/2 + Sqrt[2])], {n, 1, z}]  (* A137803 *)
v1 = Complement[Range[Max[v]], v]     (* A137804 *)
Intersection[u, v]    (* A356052 *)
Intersection[u, v1]   (* A356053 *)
Intersection[u1, v]   (* A356054 *)
Intersection[u1, v1]  (* A356055 *)