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A356059 a(n) = A001952(A137804(n)).

%I A356059 #6 Aug 03 2022 23:27:54
%S A356059 6,13,20,27,34,40,47,54,61,68,78,85,92,99,105,112,119,126,133,139,146,
%T A356059 157,163,170,177,184,191,198,204,211,218,228,235,242,249,256,262,269,
%U A356059 276,283,290,297,307,314,320,327,334,341,348,355,361,368,375,385,392
%N A356059 a(n) = A001952(A137804(n)).
%C A356059 This is the fourth of four sequences that partition the positive integers. See A356056.
%F A356059 a(n) = A001952(A137804(n)).
%e A356059 (1)  u o v = (1, 4, 7, 9, 12, 15, 18, 21, 24, 26, 29, 31, ...) = A356056
%e A356059 (2)  u o v' = (2, 5, 8, 11, 14, 16, 19, 22, 25, 28, 32, 35, ...) = A356057
%e A356059 (3)  u' o v = (3, 10, 17, 23, 30, 37, 44, 51, 58, 64, 71, ...) = A356058
%e A356059 (4)  u' o v' = (6, 13, 20, 27, 34, 40, 47, 54, 61, 68, 78, ...) = A356059
%t A356059 u = Table[Floor[n (Sqrt[2])], {n, 1, z}]   (* A001951 *)
%t A356059 u1 = Complement[Range[Max[u]], u]     (* A001952 *)
%t A356059 v = Table[Floor[n (1/2 + Sqrt[2])], {n, 1, z}]  (* A137803 *)
%t A356059 v1 = Complement[Range[Max[v]], v]  (* A137804 *)
%t A356059 Table[u[[v[[n]]]], {n, 1, z/8}];   (* A356056 *)
%t A356059 Table[u[[v1[[n]]]], {n, 1, z/8}];  (* A356057 *)
%t A356059 Table[u1[[v[[n]]]], {n, 1, z/8}];  (* A356058 *)
%t A356059 Table[u1[[v1[[n]]]], {n, 1, z/8}]; (* A356059 *)
%Y A356059 Cf. A001951, A001952, A136803, A137804, A356052 (intersections instead of results of composition), A356056, A356057, A356058.
%K A356059 nonn,easy
%O A356059 1,1
%A A356059 _Clark Kimberling_, Jul 26 2022