A356182 a(n) = A022838(A001952(n)).

5, 10, 17, 22, 29, 34, 39, 46, 51, 58, 64, 69, 76, 81, 88, 93, 100, 105, 110, 117, 122, 129, 135, 140, 147, 152, 159, 164, 171, 176, 181, 188, 193, 200, 206, 211, 218, 223, 230, 235, 240, 247, 252, 259, 265, 271, 277, 282, 289, 294, 301, 306, 311, 318, 323

Offset: 1

Author

Clark Kimberling, Aug 24 2022

Keywords

• nonn
• easy

Comments

This is the third of four sequences that partition the positive integers. See A356180.

Examples

			(1)  v o u = (1, 3, 6, 8, 12, 13, 15, 19, 20, 24, 25, 27, 31, 32, ...) = A356180
(2)  v' o u = (2, 4, 9, 11, 16, 18, 21, 26, 28, 33, 35, 37, 42, 44, ...) = A356181
(3)  v o u' = (5, 10, 17, 22, 29, 34, 39, 46, 51, 58, 64, 69, 76, ...) = A356182
(4)  v' o u' = (7, 14, 23, 30, 40, 47, 54, 63, 70, 80, 87, 94, 104, ...) = A356183
		

Crossrefs

Cf. A001951, A001952, A022838, A054406, A346308 (intersections), A356088 (reverse composites), A356180, A356181, A356183.

Programs

Mathematica

z = 800; zz = 100;
u = Table[Floor[n*Sqrt[2]], {n, 1, z}];  (* A001951 *)
u1 = Complement[Range[Max[u]], u];       (* A001952 *)
v = Table[Floor[n*Sqrt[3]], {n, 1, z}];  (* A022838 *)
v1 = Complement[Range[Max[v]], v];  (* A054406 *)
Table[v[[u[[n]]]], {n, 1, zz}]      (* A356180 *)
Table[v1[[u[[n]]]], {n, 1, zz}]     (* A356181 *)
Table[v[[u1[[n]]]], {n, 1, zz}]     (* A356182 *)
Table[v1[[u1[[n]]]], {n, 1, zz}]    (* A356183 *)

Python

from math import isqrt
def A356182(n): return isqrt(3*((k:=n<<1)+isqrt(k*n))**2) # Chai Wah Wu, Sep 05 2022