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

%I A356182 #11 Mar 23 2025 18:40:03
%S A356182 5,10,17,22,29,34,39,46,51,58,64,69,76,81,88,93,100,105,110,117,122,
%T A356182 129,135,140,147,152,159,164,171,176,181,188,193,200,206,211,218,223,
%U A356182 230,235,240,247,252,259,265,271,277,282,289,294,301,306,311,318,323
%N A356182 a(n) = A022838(A001952(n)).
%C A356182 This is the third of four sequences that partition the positive integers. See A356180.
%e A356182 (1)  v o u = (1, 3, 6, 8, 12, 13, 15, 19, 20, 24, 25, 27, 31, 32, ...) = A356180
%e A356182 (2)  v' o u = (2, 4, 9, 11, 16, 18, 21, 26, 28, 33, 35, 37, 42, 44, ...) = A356181
%e A356182 (3)  v o u' = (5, 10, 17, 22, 29, 34, 39, 46, 51, 58, 64, 69, 76, ...) = A356182
%e A356182 (4)  v' o u' = (7, 14, 23, 30, 40, 47, 54, 63, 70, 80, 87, 94, 104, ...) = A356183
%t A356182 z = 800; zz = 100;
%t A356182 u = Table[Floor[n*Sqrt[2]], {n, 1, z}];  (* A001951 *)
%t A356182 u1 = Complement[Range[Max[u]], u];       (* A001952 *)
%t A356182 v = Table[Floor[n*Sqrt[3]], {n, 1, z}];  (* A022838 *)
%t A356182 v1 = Complement[Range[Max[v]], v];  (* A054406 *)
%t A356182 Table[v[[u[[n]]]], {n, 1, zz}]      (* A356180 *)
%t A356182 Table[v1[[u[[n]]]], {n, 1, zz}]     (* A356181 *)
%t A356182 Table[v[[u1[[n]]]], {n, 1, zz}]     (* A356182 *)
%t A356182 Table[v1[[u1[[n]]]], {n, 1, zz}]    (* A356183 *)
%o A356182 (Python)
%o A356182 from math import isqrt
%o A356182 def A356182(n): return isqrt(3*((k:=n<<1)+isqrt(k*n))**2) # _Chai Wah Wu_, Sep 05 2022
%Y A356182 Cf. A001951, A001952, A022838, A054406, A346308 (intersections), A356088 (reverse composites), A356180, A356181, A356183.
%K A356182 nonn,easy
%O A356182 1,1
%A A356182 _Clark Kimberling_, Aug 24 2022