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a(n) = A001952(A137804(n)).
8

%I #6 Aug 03 2022 23:27:54

%S 6,13,20,27,34,40,47,54,61,68,78,85,92,99,105,112,119,126,133,139,146,

%T 157,163,170,177,184,191,198,204,211,218,228,235,242,249,256,262,269,

%U 276,283,290,297,307,314,320,327,334,341,348,355,361,368,375,385,392

%N a(n) = A001952(A137804(n)).

%C This is the fourth of four sequences that partition the positive integers. See A356056.

%F a(n) = A001952(A137804(n)).

%e (1) u o v = (1, 4, 7, 9, 12, 15, 18, 21, 24, 26, 29, 31, ...) = A356056

%e (2) u o v' = (2, 5, 8, 11, 14, 16, 19, 22, 25, 28, 32, 35, ...) = A356057

%e (3) u' o v = (3, 10, 17, 23, 30, 37, 44, 51, 58, 64, 71, ...) = A356058

%e (4) u' o v' = (6, 13, 20, 27, 34, 40, 47, 54, 61, 68, 78, ...) = A356059

%t u = Table[Floor[n (Sqrt[2])], {n, 1, z}] (* A001951 *)

%t u1 = Complement[Range[Max[u]], u] (* A001952 *)

%t v = Table[Floor[n (1/2 + Sqrt[2])], {n, 1, z}] (* A137803 *)

%t v1 = Complement[Range[Max[v]], v] (* A137804 *)

%t Table[u[[v[[n]]]], {n, 1, z/8}]; (* A356056 *)

%t Table[u[[v1[[n]]]], {n, 1, z/8}]; (* A356057 *)

%t Table[u1[[v[[n]]]], {n, 1, z/8}]; (* A356058 *)

%t Table[u1[[v1[[n]]]], {n, 1, z/8}]; (* A356059 *)

%Y Cf. A001951, A001952, A136803, A137804, A356052 (intersections instead of results of composition), A356056, A356057, A356058.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Jul 26 2022