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%I #5 Jan 28 2023 12:36:02
%S 6,9,10,15,16,19,24,27,28,31,36,37,42,45,46,51,52,55,60,61,66,69,70,
%T 73,78,81,82,87,88,91,96,99,100,103,108,109,114,117,118,121,126,129,
%U 130,135,136,139,144,145,150,153,154,159,160,163,168,171,172,175
%N Intersection of A026430 and (1 + A285953).
%C This is the first of three sequences that partition the positive integers. Taking u = A026430 and v = 1 + A285953 (which is A285953 except for its initial 1), the three sequences are (1) u ^ v = intersection of u and v (in increasing order); (2) u ^ v'; and (3) u' ^ v. The limiting density of each of these is 1/3.
%e (1) u ^ v = (6, 9, 10, 15, 16, 19, 24, 27, 28, 31, 36, 37, ...) = A359277
%e (2) u ^ v' = (1, 3, 5, 8, 12, 14, 18, 21, 23, 26, 30, 33, 35, ...) = A285953, except for the initial 1
%e (3) u' ^ v = (2, 4, 7, 11, 13, 17, 20, 22, 25, 29, 32, 34, 38, ...) = A356133
%t z = 200;
%t u = Accumulate[1 + ThueMorse /@ Range[0, z]] (* A026430 *)
%t u1 = Complement[Range[Max[u]], u] (* A356133 *)
%t v = u + 1
%t v1 = Complement[Range[Max[v]], v]
%t Intersection[u, v] (* A359277 *)
%t Intersection[u, v1] (* A285953 *)
%t Intersection[u1, v] (* A356133 *)
%Y Cf. A026530, A285954, A356133, A359352 to A360139) (results of compositions instead of intersections).
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, Jan 26 2023
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