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A356086 Intersection of A001952 and A022838.

%I A356086 #11 Aug 06 2022 19:07:20
%S A356086 3,6,10,13,17,20,27,34,51,58,64,71,81,88,95,102,105,109,112,116,119,
%T A356086 122,126,129,133,136,143,150,157,174,180,187,204,211,218,221,225,228,
%U A356086 232,235,242,245,249,252,256,259,266,273,284,285,287,289,290,292,294
%N A356086 Intersection of A001952 and A022838.
%C A356086 This is the third of four sequences, u^v, u^v', u'^v, u'^v', that partition the positive integers. See A346308.
%e A356086 (1)  u ^ v   = ( 1,  5,  8, 12, 15, 19, 22, 24, 25, 29, 31, 32, ...) = A346308
%e A356086 (2)  u ^ v'  = ( 2,  4,  7,  9, 11, 14, 16, 18, 21, 26, 28, 33, ...) = A356085
%e A356086 (3)  u' ^ v  = ( 3,  6, 10, 13, 17, 20, 27, 34, 51, 58, 64, 71, ...) = A356086
%e A356086 (4)  u' ^ v' = (23, 30, 37, 40, 44, 47, 54, 61, 68, 75, 78, 85, ...) = A356087
%t A356086 z = 200;
%t A356086 r = Sqrt[2]; u = Table[Floor[n*r], {n, 1, z}]  (* A001951 *)
%t A356086 u1 = Take[Complement[Range[1000], u], z]  (* A001952 *)
%t A356086 r1 = Sqrt[3]; v = Table[Floor[n*r1], {n, 1, z}]  (* A022838 *)
%t A356086 v1 = Take[Complement[Range[1000], v], z]  (* A054406 *)
%t A356086 Intersection[u, v]    (* A346308 *)
%t A356086 Intersection[u, v1]   (* A356085 *)
%t A356086 Intersection[u1, v]   (* A356086 *)
%t A356086 Intersection[u1, v1]  (* A356087 *)
%o A356086 (Python)
%o A356086 from math import isqrt
%o A356086 from itertools import count, islice
%o A356086 def A356086_gen(): # generator of terms
%o A356086     return filter(lambda n:n == isqrt(3*(isqrt(n**2//3)+1)**2),((k:=n<<1)+isqrt(k*n) for n in count(1)))
%o A356086 A356086_list = list(islice(A356086_gen(),30)) # _Chai Wah Wu_, Aug 06 2022
%Y A356086 Cf. A001951, A001952, A022838, A054406, A346308, A356085, A356087, A356088 (results of composition instead of intersections).
%K A356086 nonn,easy
%O A356086 1,1
%A A356086 _Clark Kimberling_, Aug 04 2022