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A356139 a(n) = A137804(A001951(n)).

%I A356139 #14 Mar 23 2025 04:34:27
%S A356139 2,4,8,10,14,16,18,23,25,29,31,33,37,39,43,46,50,52,54,58,60,64,67,69,
%T A356139 73,75,79,81,85,87,90,94,96,100,102,104,108,110,115,117,119,123,125,
%U A356139 129,131,136,138,140,144,146,150,152,154,159,161,165,167,171,173
%N A356139 a(n) = A137804(A001951(n)).
%C A356139 This is the second of four sequences that partition the positive integers. See A356138.
%e A356139 (1)  v o u   = (1,  3,  7,  9, 13, 15, 17, 21, 22, 26, 28, 30, 34, ...) = A356138
%e A356139 (2)  v' o u  = (2,  4,  8, 10, 14, 16, 18, 23, 25, 29, 31, 33, 37, ...) = A356139
%e A356139 (3)  v o u'  = (5, 11, 19, 24, 32, 38, 44, 51, 57, 65, 70, 76, 84, ...) = A356140
%e A356139 (4)  v' o u' = (6, 12, 20, 27, 35, 41, 48, 56, 62, 71, 77, 83, 92, ...) = A356141
%t A356139 z = 800;
%t A356139 u = Table[Floor[n (Sqrt[2])], {n, 1, z}];   (*A001951*)
%t A356139 u1 = Complement[Range[Max[u]], u] ;    (*A001952*)
%t A356139 v = Table[Floor[n (1/2 + Sqrt[2])], {n, 1, z}];  (*A137803*)
%t A356139 v1 = Complement[Range[Max[v]], v] ;     (*A137804*)
%t A356139 Table[v[[u[[n]]]], {n, 1, z/8}]   (*A356138 *)
%t A356139 Table[v1[[u[[n]]]], {n, 1, z/8}]  (* A356139*)
%t A356139 Table[v[[u1[[n]]]], {n, 1, z/8}]  (* A356140 *)
%t A356139 Table[v1[[u1[[n]]]], {n, 1, z/8}] (* A356141 *)
%Y A356139 Cf. A001951, A001952, A137804.
%Y A356139 Cf. A356056, A356057, A356058, A356059, A356138, A356140, A356141.
%K A356139 nonn,easy
%O A356139 1,1
%A A356139 _Clark Kimberling_, Aug 06 2022