A356056 -id:A356056 - cp's OEIS frontend

A356140 a(n) = A137803(A001952(n)).

5, 11, 19, 24, 32, 38, 44, 51, 57, 65, 70, 76, 84, 89, 97, 103, 111, 116, 122, 130, 135, 143, 149, 155, 162, 168, 176, 181, 189, 195, 200, 208, 214, 222, 227, 233, 241, 246, 254, 260, 266, 273, 279, 287, 292, 300, 306, 312, 319, 325, 333, 338, 344, 352, 357

Offset: 1

Clark Kimberling, Aug 06 2022

This is the third of four sequences that partition the positive integers. See A356138.

			(1)  v o u   = (1,  3,  7,  9, 13, 15, 17, 21, 22, 26, 28, 30, 34, ...) = A356138
(2)  v' o u  = (2,  4,  8, 10, 14, 16, 18, 23, 25, 29, 31, 33, 37, ...) = A356139
(3)  v o u'  = (5, 11, 19, 24, 32, 38, 44, 51, 57, 65, 70, 76, 84, ...) = A356140
(4)  v' o u' = (6, 12, 20, 27, 35, 41, 48, 56, 62, 71, 77, 83, 92, ...) = A356141

Cf. A001951, A001952, A137804.

Cf. A356056, A356057, A356058, A356059, A356138, A356139, A356141.

z = 800;
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[v[[u[[n]]]], {n, 1, z/8}]   (*A356138 *)
Table[v1[[u[[n]]]], {n, 1, z/8}]  (* A356139*)
Table[v[[u1[[n]]]], {n, 1, z/8}]  (* A356140 *)
Table[v1[[u1[[n]]]], {n, 1, z/8}] (* A356141 *)

A356141 a(n) = A137804(A001952(n)).

Original entry on oeis.org

6, 12, 20, 27, 35, 41, 48, 56, 62, 71, 77, 83, 92, 98, 106, 113, 121, 127, 134, 142, 148, 157, 163, 169, 177, 184, 192, 198, 207, 213, 219, 228, 234, 242, 249, 255, 263, 270, 278, 284, 291, 299, 305, 314, 320, 328, 335, 341, 349, 355, 364, 370, 376, 385, 391

Offset: 1

Clark Kimberling, Aug 06 2022

This is the fourth of four sequences that partition the positive integers. See A356138.

			(1)  v o u   = (1,  3,  7,  9, 13, 15, 17, 21, 22, 26, 28, 30, 34, ...) = A356138
(2)  v' o u  = (2,  4,  8, 10, 14, 16, 18, 23, 25, 29, 31, 33, 37, ...) = A356139
(3)  v o u'  = (5, 11, 19, 24, 32, 38, 44, 51, 57, 65, 70, 76, 84, ...) = A356140
(4)  v' o u' = (6, 12, 20, 27, 35, 41, 48, 56, 62, 71, 77, 83, 92, ...) = A356141

Cf. A001951, A001952, A137804.

Cf. A356056, A356057, A356058, A356059, A356138, A356139, A356140.

z = 800;
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[v[[u[[n]]]], {n, 1, z/8}]   (*A356138 *)
Table[v1[[u[[n]]]], {n, 1, z/8}]  (* A356139*)
Table[v[[u1[[n]]]], {n, 1, z/8}]  (* A356140 *)
Table[v1[[u1[[n]]]], {n, 1, z/8}] (* A356141 *)

cp's OEIS Frontend

A356140 a(n) = A137803(A001952(n)).

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