A360405 - OEIS

A360405

a(n) = A360393(A356133(n)).

2, 6, 15, 27, 34, 45, 55, 60, 69, 81, 91, 96, 108, 114, 124, 135, 142, 153, 163, 168, 180, 186, 195, 208, 217, 222, 231, 244, 249, 262, 271, 276, 285, 297, 307, 312, 324, 330, 339, 352, 361, 366, 375, 387, 394, 405, 414, 421, 432, 438, 447, 459, 466, 477

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OFFSET

1,1

COMMENTS

This is the fourth 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 (and likewise for A360394-A360401).

LINKS

Table of n, a(n) for n=1..54.

EXAMPLE

(1) v o u = (3, 7, 10, 11, 14, 16, 17, 20, 23, 25, 26, 29, 30, 33, 37, ...) = A360402

(2) v' o u = (1, 4, 9, 13, 19, 22, 24, 31, 36, 40, 42, 49, 51, 58, 64, ...) = A360403

(3) v o u' = (5, 8, 12, 18, 21, 28, 32, 35, 39, 46, 50, 53, 59, 62, 67, ...) = A360404

(4) v' o u' = (2, 6, 15, 27, 34, 45, 55, 60, 69, 81, 91, 96, 108, 114, ...) = A360405

MATHEMATICA

z = 2000; zz = 100;

u = Accumulate[1 + ThueMorse /@ Range[0, 600]]; (* A026430 *)

u1 = Complement[Range[Max[u]], u]; (* A356133 *)

v = u + 2; (* A360392 *)

v1 = Complement[Range[Max[v]], v]; (* A360393 *)

Table[v[[u[[n]]]], {n, 1, zz}] (* A360402 *)

Table[v1[[u[[n]]]], {n, 1, zz} (* A360403 *)

Table[v[[u1[[n]]]], {n, 1, zz}] (* A360404 *)

Table[v1[[u1[[n]]]], {n, 1, zz}] (* A360405 *)

CROSSREFS

Cf. A026530, A360392, A360393, A360394-A3546352 (intersections instead of results of compositions), A360398-A360401 (results of reversed compositions), A360402, A360403, A360404.

Sequence in context: A269706 A293402 A192691 * A256313 A380921 A138621

Adjacent sequences: A360402 A360403 A360404 * A360406 A360407 A360408

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 01 2023

STATUS

approved