A356058 a(n) = A001952(A137803(n)).

3, 10, 17, 23, 30, 37, 44, 51, 58, 64, 71, 75, 81, 88, 95, 102, 109, 116, 122, 129, 136, 143, 150, 153, 160, 167, 174, 180, 187, 194, 201, 208, 215, 221, 225, 232, 238, 245, 252, 259, 266, 273, 279, 286, 293, 300, 303, 310, 317, 324, 331, 338, 344, 351, 358

Offset

1,1

Comments

This is the third of four sequences that partition the positive integers. See A356056.

Links

Table of n, a(n) for n=1..55.

Formula

a(n) = A001952(A137803(n)).

Example

(1)  u o v   = (1,  4,  7,  9, 12, 15, 18, 21, 24, 26, 29, ...) = A356056
(2)  u o v'  = (2,  5,  8, 11, 14, 16, 19, 22, 25, 28, 32, ...) = A356057
(3)  u' o v  = (3, 10, 17, 23, 30, 37, 44, 51, 58, 64, 71, ...) = A356058
(4)  u' o v' = (6, 13, 20, 27, 34, 40, 47, 54, 61, 68, 78, ...) = A356059

Mathematica

u = Table[Floor[n (Sqrt[2])], {n, 1, z}]   (* A001951 *)
u1 = Complement[Range[Max[u]], u]     (* A001952 *)
v = Table[Floor[n (1/2 + Sqrt[2])], {n, 1, z}]  (* A137803 *)
v1 = Complement[Range[Max[v]], v]  (* A137804 *)
Table[u[[v[[n]]]], {n, 1, z/8}];   (* A356056 *)
Table[u[[v1[[n]]]], {n, 1, z/8}];  (* A356057 *)
Table[u1[[v[[n]]]], {n, 1, z/8}];  (* A356058 *)
Table[u1[[v1[[n]]]], {n, 1, z/8}]; (* A356059 *)

Crossrefs

Cf. A001951, A001952, A136803, A137804, A356052 (intersections instead of the results of composition), A356056, A356057, A356059.

Sequence in context: A296219 A063293 A270997 * A342280 A024981 A003072

Adjacent sequences: A356055 A356056 A356057 * A356059 A356060 A356061

Keyword

nonn,easy

Author

Clark Kimberling, Jul 26 2022

Status

approved