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A356089 a(n) = A001951(A054406(n)).

%I A356089 #19 Mar 23 2025 04:33:18
%S A356089 2,5,9,12,15,19,22,25,29,32,36,39,42,46,49,52,56,59,62,66,69,73,76,79,
%T A356089 83,86,89,93,96,98,103,106,110,113,115,120,123,125,130,132,137,140,
%U A356089 142,147,149,152,156,159,162,166,169,173,176,179,183,186,189,193
%N A356089 a(n) = A001951(A054406(n)).
%C A356089 This is the second of four sequences that partition the positive integers. See A356088.
%e A356089 (1)  u o v   = (1,  4,  7,  8, 11, 14, 16, 18, 21, 24, 26, ...) = A356088.
%e A356089 (2)  u o v'  = (2,  5,  9, 12, 15, 19, 22, 25, 29, 32, 36, ...) = A356089.
%e A356089 (3)  u' o v  = (3, 10, 17, 20, 27, 34, 40, 44, 51, 58, 64, ...) = A356090.
%e A356089 (4)  u' o v' = (6, 13, 23, 30, 37, 47, 54, 61, 71, 78, 88, ...) = A356091.
%t A356089 z = 600; zz = 100;
%t A356089 u = Table[Floor[n*Sqrt[2]], {n, 1, z}];  (* A001951 *)
%t A356089 u1 = Complement[Range[Max[u]], u];  (* A001952 *)
%t A356089 v = Table[Floor[n*Sqrt[3]], {n, 1, z}];  (* A022838 *)
%t A356089 v1 = Complement[Range[Max[v]], v];  (* A054406 *)
%t A356089 Table[u[[v[[n]]]], {n, 1, zz}]    (* A356088 *)
%t A356089 Table[u[[v1[[n]]]], {n, 1, zz}]   (* A356089 *)
%t A356089 Table[u1[[v[[n]]]], {n, 1, zz}]   (* A356090 *)
%t A356089 Table[u1[[v1[[n]]]], {n, 1, zz}]  (* A356091 *)
%Y A356089 Cf. A001951, A001952, A022838, A054406, A346308 (intersections instead of results of composition), A356088, A356090, A356091.
%K A356089 nonn,easy
%O A356089 1,1
%A A356089 _Clark Kimberling_, Aug 04 2022