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A356090 a(n) = A001952(A022838(n)).

%I A356090 #17 Mar 23 2025 04:34:16
%S A356090 3,10,17,20,27,34,40,44,51,58,64,68,75,81,85,92,99,105,109,116,122,
%T A356090 129,133,139,146,153,157,163,170,174,180,187,194,198,204,211,218,221,
%U A356090 228,235,242,245,252,259,262,269,276,283,286,293,300,307,310,317,324
%N A356090 a(n) = A001952(A022838(n)).
%C A356090 This is the third of four sequences that partition the positive integers. See A356088.
%e A356090 (1)  u o v   = (1,  4,  7,  8, 11, 14, 16, 18, 21, 24, 26, ...) = A356088
%e A356090 (2)  u o v'  = (2,  5,  9, 12, 15, 19, 22, 25, 29, 32, 36, ...) = A356089
%e A356090 (3)  u' o v  = (3, 10, 17, 20, 27, 34, 40, 44, 51, 58, 64, ...) = A356090
%e A356090 (4)  u' o v' = (6, 13, 23, 30, 37, 47, 54, 61, 71, 78, 88, ...) = A356091
%t A356090 z = 600; zz = 100;
%t A356090 u = Table[Floor[n*Sqrt[2]], {n, 1, z}];  (* A001951 *)
%t A356090 u1 = Complement[Range[Max[u]], u];  (* A001952 *)
%t A356090 v = Table[Floor[n*Sqrt[3]], {n, 1, z}];  (* A022838 *)
%t A356090 v1 = Complement[Range[Max[v]], v];  (* A054406 *)
%t A356090 Table[u[[v[[n]]]], {n, 1, zz}]    (* A356088 *)
%t A356090 Table[u[[v1[[n]]]], {n, 1, zz}]   (* A356089 *)
%t A356090 Table[u1[[v[[n]]]], {n, 1, zz}]   (* A356090 *)
%t A356090 Table[u1[[v1[[n]]]], {n, 1, zz}]  (* A356091 *)
%Y A356090 Cf. A001951, A001952, A022838, A054406, A346308 (intersections instead of results of composition), A356088, A356089, A356091.
%K A356090 nonn,easy
%O A356090 1,1
%A A356090 _Clark Kimberling_, Aug 04 2022