A359277 Intersection of A026430 and (1 + A285953).

6, 9, 10, 15, 16, 19, 24, 27, 28, 31, 36, 37, 42, 45, 46, 51, 52, 55, 60, 61, 66, 69, 70, 73, 78, 81, 82, 87, 88, 91, 96, 99, 100, 103, 108, 109, 114, 117, 118, 121, 126, 129, 130, 135, 136, 139, 144, 145, 150, 153, 154, 159, 160, 163, 168, 171, 172, 175

Offset: 1

Author

Clark Kimberling, Jan 26 2023

Keywords

• nonn
• easy

Comments

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.

Examples

			(1)  u ^ v = (6, 9, 10, 15, 16, 19, 24, 27, 28, 31, 36, 37, ...) =    A359277
(2)  u ^ v' = (1, 3, 5, 8, 12, 14, 18, 21, 23, 26, 30, 33, 35, ...) =  A285953, except for the initial 1
(3)  u' ^ v = (2, 4, 7, 11, 13, 17, 20, 22, 25, 29, 32, 34, 38, ...) = A356133
		

Crossrefs

Cf. A026530, A285954, A356133, A359352 to A360139) (results of compositions instead of intersections).

Programs

Mathematica

z = 200;
u = Accumulate[1 + ThueMorse /@ Range[0, z]]   (* A026430 *)
u1 = Complement[Range[Max[u]], u]  (* A356133 *)
v = u + 1
v1 = Complement[Range[Max[v]], v]
Intersection[u, v]    (* A359277 *)
Intersection[u, v1]   (* A285953 *)
Intersection[u1, v]   (* A356133 *)