cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A356139 a(n) = A137804(A001951(n)).

Original entry on oeis.org

2, 4, 8, 10, 14, 16, 18, 23, 25, 29, 31, 33, 37, 39, 43, 46, 50, 52, 54, 58, 60, 64, 67, 69, 73, 75, 79, 81, 85, 87, 90, 94, 96, 100, 102, 104, 108, 110, 115, 117, 119, 123, 125, 129, 131, 136, 138, 140, 144, 146, 150, 152, 154, 159, 161, 165, 167, 171, 173
Offset: 1

Views

Author

Clark Kimberling, Aug 06 2022

Keywords

Comments

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

Examples

			(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

Crossrefs

Cf. A001951, A001952, A137804.
Cf. A356056, A356057, A356058, A356059, A356138, A356140, A356141.

Programs

  • Mathematica
    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 *)

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

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Aug 06 2022

Keywords

Comments

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

Examples

			(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

Crossrefs

Cf. A001951, A001952, A137804.
Cf. A356056, A356057, A356058, A356059, A356138, A356139, A356141.

Programs

  • Mathematica
    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

Views

Author

Clark Kimberling, Aug 06 2022

Keywords

Comments

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

Examples

			(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

Crossrefs

Cf. A001951, A001952, A137804.
Cf. A356056, A356057, A356058, A356059, A356138, A356139, A356140.

Programs

  • Mathematica
    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 *)
Showing 1-3 of 3 results.

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