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A356085 Intersection of A001951 and A054406.

%I A356085 #5 Aug 03 2022 23:28:12
%S A356085 2,4,7,9,11,14,16,18,21,26,28,33,35,42,49,52,56,59,63,66,70,73,80,82,
%T A356085 87,89,94,97,101,104,106,108,111,113,115,118,120,123,125,127,130,132,
%U A356085 134,137,141,144,149,151,156,158,165,172,175,179,182,186,189,196
%N A356085 Intersection of A001951 and A054406.
%C A356085 This is the second of four sequences, u^v, u^v', u'^v, u'^v', that partition the positive integers. See A346308.
%e A356085 (1)  u ^ v = (1, 5, 8, 12, 15, 19, 22, 24, 25, 29, 31, 32, ...) =  A346308
%e A356085 (2)  u ^ v' = (2, 4, 7, 9, 11, 14, 16, 18, 21, 26, 28, 33, 35, ...) =  A356085
%e A356085 (3)  u' ^ v = (3, 6, 10, 13, 17, 20, 27, 34, 51, 58, 64, 71, 81, ...) = A356086
%e A356085 (4)  u' ^ v' = (23, 30, 37, 40, 44, 47, 54, 61, 68, 75, 78, 85, ...) = A356087
%t A356085 z = 200;
%t A356085 r = Sqrt[2]; u = Table[Floor[n*r], {n, 1, z}]  (* A001951 *)
%t A356085 u1 = Take[Complement[Range[1000], u], z]  (* A001952 *)
%t A356085 r1 = Sqrt[3]; v = Table[Floor[n*r1], {n, 1, z}]  (* A022838 *)
%t A356085 v1 = Take[Complement[Range[1000], v], z]  (* A054406 *)
%t A356085 t1 = Intersection[u, v]    (* A346308 *)
%t A356085 t2 = Intersection[u, v1]   (* A356085 *)
%t A356085 t3 = Intersection[u1, v]   (* A356086 *)
%t A356085 t4 = Intersection[u1, v1]  (* A356087 *)
%Y A356085 Cf. A001951, A001952, A022838, A054406, A346308, A356086, A356087, A356088 (composites instead of intersections).
%K A356085 nonn,easy
%O A356085 1,1
%A A356085 _Clark Kimberling_, Jul 26 2022