cp's OEIS Frontend

A360399 a(n) = A026430(1 + A360393(n)).

%I A360399 #4 Mar 04 2023 15:26:35
%S A360399 1,3,6,9,14,19,23,28,33,36,41,46,51,54,60,63,68,73,77,82,87,90,96,99,
%T A360399 103,109,114,117,121,128,130,136,141,144,149,154,159,162,168,171,175,
%U A360399 181,186,189,194,199,203,209,213,216,222,225,230,235,239,245,249
%N A360399 a(n) = A026430(1 + A360393(n)).
%C A360399 This is the second of four sequences that partition the positive integers. Suppose that u = (u(n)) and v = (v(n)) are increasing sequences of positive integers.   Let u' and v' be their (increasing) complements, and consider these four sequences:
%C A360399 (1) u o v, defined by (u o v)(n)  = u(v(n));
%C A360399 (2) u o v';
%C A360399 (3) u' o v;
%C A360399 (4) v' o u'.
%C A360399 Every positive integer is in exactly one of the four sequences. Their limiting densities are 4/9, 2/9, 2/9, 1/9 (and likewise for A360394-A360397 and A360402-A360405).
%e A360399 (1)  u o v = (5, 8, 10, 12, 15, 16, 18, 21, 24, 26, 27, 30, 31, 35, 37, 39, ...) = A360398
%e A360399 (2)  u o v' = (1, 3, 6, 9, 14, 19, 23, 28, 33, 36, 41, 46, 51, 54, 60, 63, 68, ...) = A360399
%e A360399 (3)  u' o v = (7, 13, 20, 22, 29, 32, 34, 40, 47, 49, 53, 58, 62, 67, 74, 76, ...) = A360400
%e A360399 (4)  u' o v' = (2, 4, 11, 17, 25, 38, 43, 56, 64, 71, 79, 92, 101, 106, 119, ...) = A360401
%t A360399 z = 2000;
%t A360399 u = Accumulate[1 + ThueMorse /@ Range[0, 600]]; (* A026430 *)
%t A360399 u1 = Complement[Range[Max[u]], u];  (* A356133 *)
%t A360399 v = u + 2;  (* A360392 *)
%t A360399 v1 = Complement[Range[Max[v]], v];    (* A360393 *)
%t A360399 zz = 100;
%t A360399 Table[u[[v[[n]]]], {n, 1, zz}]    (* A360398 *)
%t A360399 Table[u[[v1[[n]]]], {n, 1, zz}]   (* A360399 *)
%t A360399 Table[u1[[v[[n]]]], {n, 1, zz}]   (* A360400 *)
%t A360399 Table[u1[[v1[[n]]]], {n, 1, zz}]  (* A360401 *)
%Y A360399 Cf. A026530, A356133, A360392, A360393, A360398, A286355, A286356, A360394 (intersections instead of results of composition), A360402-A360405.
%K A360399 nonn,easy
%O A360399 1,2
%A A360399 _Clark Kimberling_, Feb 10 2023