cp's OEIS Frontend

A356087 Intersection of A001952 and A054406.

%I A356087 #7 Aug 05 2022 07:42:26
%S A356087 23,30,37,40,44,47,54,61,68,75,78,85,92,99,139,146,153,160,163,167,
%T A356087 170,177,184,191,194,198,201,208,215,238,262,269,276,279,283,286,288,
%U A356087 291,293,295,298,300,302,305,307,309,312,314,317,319,321,324,326,328
%N A356087 Intersection of A001952 and A054406.
%C A356087 This is the fourth of four sequences, u^v, u^v', u'^v, u'^v', that partition the positive integers. See A346308.
%e A356087 (1)  u ^ v   = ( 1,  5,  8, 12, 15, 19, 22, 24, 25, 29, 31, 32, ...) = A346308.
%e A356087 (2)  u ^ v'  = ( 2,  4,  7,  9, 11, 14, 16, 18, 21, 26, 28, 33, ...) = A356085.
%e A356087 (3)  u' ^ v  = ( 3,  6, 10, 13, 17, 20, 27, 34, 51, 58, 64, 71, ...) = A356086.
%e A356087 (4)  u' ^ v' = (23, 30, 37, 40, 44, 47, 54, 61, 68, 75, 78, 85, ...) = A356087.
%t A356087 r = Sqrt[2]; u = Table[Floor[n*r], {n, 1, z}]  (* A001951 *)
%t A356087 u1 = Take[Complement[Range[1000], u], z]  (* A001952 *)
%t A356087 r1 = Sqrt[3]; v = Table[Floor[n*r1], {n, 1, z}]  (* A022838 *)
%t A356087 v1 = Take[Complement[Range[1000], v], z]  (* A054406 *)
%t A356087 Intersection[u, v]    (* A346308 *)
%t A356087 Intersection[u, v1]   (* A356085 *)
%t A356087 Intersection[u1, v]   (* A356086 *)
%t A356087 Intersection[u1, v1]  (* A356087 *)
%Y A356087 Cf. A001951, A001952, A022838, A054406, A346308, A356085, A356086, A356088 (results of composition instead of intersections).
%K A356087 nonn,easy
%O A356087 1,1
%A A356087 _Clark Kimberling_, Aug 04 2022