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A356057 a(n) = A001951(A137804(n)).

%I A356057 #6 Aug 03 2022 23:27:40
%S A356057 2,5,8,11,14,16,19,22,25,28,32,35,38,41,43,46,49,52,55,57,60,65,67,70,
%T A356057 73,76,79,82,84,87,90,94,97,100,103,106,108,111,114,117,120,123,127,
%U A356057 130,132,135,138,141,144,147,149,152,155,159,162,165,168,171,173
%N A356057 a(n) = A001951(A137804(n)).
%C A356057 This is the second of four sequences that partition the positive integers. See A356056.
%F A356057 a(n) = A001951(A137804(n)).
%e A356057 (1)  u o v = (1, 4, 7, 9, 12, 15, 18, 21, 24, 26, 29, 31, ...) = A356056
%e A356057 (2)  u o v' = (2, 5, 8, 11, 14, 16, 19, 22, 25, 28, 32, 35, ...) = A356057
%e A356057 (3)  u' o v = (3, 10, 17, 23, 30, 37, 44, 51, 58, 64, 71, ...) = A356058
%e A356057 (4)  u' o v' = (6, 13, 20, 27, 34, 40, 47, 54, 61, 68, 78, ...) = A356059
%t A356057 u = Table[Floor[n (Sqrt[2])], {n, 1, z}]   (* A001951 *)
%t A356057 u1 = Complement[Range[Max[u]], u]     (* A001952 *)
%t A356057 v = Table[Floor[n (1/2 + Sqrt[2])], {n, 1, z}]  (* A137803 *)
%t A356057 v1 = Complement[Range[Max[v]], v]  (* A137804 *)
%t A356057 Table[u[[v[[n]]]], {n, 1, z/8}];   (* A356056 *)
%t A356057 Table[u[[v1[[n]]]], {n, 1, z/8}];  (* A356057 *)
%t A356057 Table[u1[[v[[n]]]], {n, 1, z/8}];  (* A356058 *)
%t A356057 Table[u1[[v1[[n]]]], {n, 1, z/8}]; (* A356059 *)
%Y A356057 Cf. A001951, A001952, A136803, A137804, A356052 (intersections instead of results of composition), A356056, A356058, A356059.
%K A356057 nonn,easy
%O A356057 1,1
%A A356057 _Clark Kimberling_, Jul 26 2022