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A356218 a(n) = A108598(A000201(n)).

%I A356218 #17 Mar 23 2025 18:39:53
%S A356218 1,5,7,10,14,16,19,21,25,28,30,34,37,39,43,45,48,52,54,57,59,63,66,68,
%T A356218 72,75,77,81,83,86,90,92,95,99,101,104,106,110,113,115,119,121,124,
%U A356218 128,130,133,137,139,142,144,148,151,153,157,159,162,166,168,171
%N A356218 a(n) = A108598(A000201(n)).
%C A356218 This is the second of four sequences that partition the positive integers. See A356217.
%e A356218 (1)  v o u = (2, 6, 8, 13, 17, 20, 24, 26, 31, 35, 38, 42, ...) = A356217
%e A356218 (2)  v' o u = (1, 5, 7, 10, 14, 16, 19, 21, 25, 28, 30, 34, ...) = A356218
%e A356218 (3)  v o u' = (4, 11, 15, 22, 29, 33, 40, 44, 51, 58, 62, 76, ...) = A190509
%e A356218 (4)  v' o u' = (3, 9, 12, 18, 23, 27, 32, 36, 41, 47, 50, 56, ...) = A356220
%t A356218 z = 1000;
%t A356218 u = Table[Floor[n*(1 + Sqrt[5])/2], {n, 1, z}];  (* A000201 *)
%t A356218 u1 = Complement[Range[Max[u]], u];  (* A001950 *)
%t A356218 v = Table[Floor[n*Sqrt[5]], {n, 1, z}];  (* A022839 *)
%t A356218 v1 = Complement[Range[Max[v]], v];  (* A108598 *)
%t A356218 zz = 120;
%t A356218 Table[v[[u[[n]]]], {n, 1, z/4}]   (* A356217 *)
%t A356218 Table[v1[[u[[n]]]], {n, 1, z/4}]  (* A356218 *)
%t A356218 Table[v[[u1[[n]]]], {n, 1, z/4}]  (* A190509 *)
%t A356218 Table[v1[[u1[[n]]]], {n, 1, z/4}] (* A356220 *)
%Y A356218 Cf. u = A000201, u' = A001950, v = A022839, v' = A108598, A351415 (intersections), A356104 (reverse composites), A356217, A190509, A356220.
%K A356218 nonn,easy
%O A356218 1,2
%A A356218 _Clark Kimberling_, Oct 02 2022