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A356091 a(n) = A001952(A054406(n)).

%I A356091 #14 Mar 23 2025 04:34:53
%S A356091 6,13,23,30,37,47,54,61,71,78,88,95,102,112,119,126,136,143,150,160,
%T A356091 167,177,184,191,201,208,215,225,232,238,249,256,266,273,279,290,297,
%U A356091 303,314,320,331,338,344,355,361,368,378,385,392,402,409,419,426,433
%N A356091 a(n) = A001952(A054406(n)).
%C A356091 This is the fourth of four sequences that partition the positive integers. See A356088.
%e A356091 (1)  u o v   = (1,  4,  7,  8, 11, 14, 16, 18, 21, 24, 26, ...) = A356088
%e A356091 (2)  u o v'  = (2,  5,  9, 12, 15, 19, 22, 25, 29, 32, 36, ...) = A356089
%e A356091 (3)  u' o v  = (3, 10, 17, 20, 27, 34, 40, 44, 51, 58, 64, ...) = A356090
%e A356091 (4)  u' o v' = (6, 13, 23, 30, 37, 47, 54, 61, 71, 78, 88, ...) = A356091
%t A356091 z = 600; zz = 100;
%t A356091 u = Table[Floor[n*Sqrt[2]], {n, 1, z}];  (* A001951 *)
%t A356091 u1 = Complement[Range[Max[u]], u];  (* A001952 *)
%t A356091 v = Table[Floor[n*Sqrt[3]], {n, 1, z}];  (* A022838 *)
%t A356091 v1 = Complement[Range[Max[v]], v];  (* A054406 *)
%t A356091 Table[u[[v[[n]]]], {n, 1, zz}]    (* A356088 *)
%t A356091 Table[u[[v1[[n]]]], {n, 1, zz}]   (* A356089 *)
%t A356091 Table[u1[[v[[n]]]], {n, 1, zz}]   (* A356090 *)
%t A356091 Table[u1[[v1[[n]]]], {n, 1, zz}]  (* A356091 *)
%Y A356091 Cf. A001951, A001952, A022838, A054406, A346308 (intersections instead of results of composition), A356088, A356089, A356090.
%K A356091 nonn,easy
%O A356091 1,1
%A A356091 _Clark Kimberling_, Aug 05 2022