

A360137


a(n) = V(A026430(n)), where V(1) = 1 and V(k) = A285953(k+1) for k >= 2.


4



1, 5, 12, 14, 21, 23, 26, 33, 39, 41, 44, 50, 54, 59, 65, 68, 75, 77, 80, 86, 90, 95, 102, 105, 107, 113, 120, 123, 128, 132, 134, 141, 147, 149, 152, 158, 162, 167, 174, 177, 179, 185, 192, 194, 201, 203, 207, 212, 216, 221, 228, 230, 237, 239, 243, 248
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OFFSET

1,2


COMMENTS

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:
(1) v o u, defined by (v o u)(n) = v(u(n));
(2) v' o u;
(3) v o u';
(4) v' o u.
Every positive integer is in exactly one of the four sequences. Their limiting densities are 4/9, 2/9, 2/9, 1/9, respectively.


LINKS



EXAMPLE

(1) v o u = (2, 6, 9, 10, 13, 15, 16, 19, 22, 24, 25, 28, 29, 32, 36, ...) = A360136
(2) v' o u = (1, 5, 12, 14, 21, 23, 26, 33, 39, 41, 44, 50, 54, 59, 65, ...) = A360137
(3) v o u' = (4, 7, 11, 17, 20, 27, 31, 34, 38, 45, 49, 52, 58, 61, 66, ...) = A360138
(4) v' o u' = (3, 8, 18, 30, 35, 48, 57, 63, 72, 84, 93, 98, 111, 116, ...) = A360139


MATHEMATICA

z = 2000; zz = 100;
u = Accumulate[1 + ThueMorse /@ Range[0, 600]]; (* A026430 *)
u1 = Complement[Range[Max[u]], u]; (* A356133 *)
v1 = Complement[Range[Max[v]], v]; (* A285953 *)
Table[v[[u[[n]]]], {n, 1, zz}] (* A360136 *)
Table[v1[[u[[n]]]], {n, 1, zz}] (* A360137 *)
Table[v[[u1[[n]]]], {n, 1, zz}] (* A360138 *)
Table[v1[[u1[[n]]]], {n, 1, zz}] (* A360139 *)


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



