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 1-5 of 5 results.

A370916 Positive integers whose ternary representation includes at least one 0, and every 0 is followed by 1.

Original entry on oeis.org

10, 19, 31, 32, 37, 46, 58, 59, 64, 73, 91, 94, 95, 97, 98, 112, 113, 118, 127, 139, 140, 145, 154, 172, 175, 176, 178, 179, 193, 194, 199, 208, 220, 221, 226, 235, 274, 275, 280, 283, 284, 286, 287, 289, 292, 293, 295, 296, 334, 337, 338, 340, 341, 355, 356
Offset: 1

Views

Author

Clark Kimberling, Mar 13 2024

Keywords

Examples

			The ternary representations of 10, 19, and 31 are 101, 201, and 1011.

Crossrefs

Cf. A007089, A081605.
Cf. A370917, A370918, A370919, A370920, A370921, A370922, A370923.

Programs

  • Mathematica
    Map[#[[1]] &, Select[Map[{#, #[[1]] > 0 && #[[1]] == #[[2]] &[{Length[
StringCases[#, "0"]], Length[StringCases[#, "01"]]}] &[
IntegerString[#, 3]]} &, Range[500]], #[[2]] &]]
 (* Peter J. C. Moses, Mar 05 2024 *)

A370918 Positive integers whose ternary representation includes at least one 1, and every 1 is followed by 0.

Original entry on oeis.org

3, 9, 11, 21, 27, 29, 30, 33, 35, 57, 63, 65, 75, 81, 83, 84, 87, 89, 90, 92, 99, 101, 102, 105, 107, 165, 171, 173, 183, 189, 191, 192, 195, 197, 219, 225, 227, 237, 243, 245, 246, 249, 251, 252, 254, 261, 263, 264, 267, 269, 270, 272, 273, 276, 278, 297
Offset: 1

Views

Author

Clark Kimberling, Mar 15 2024

Keywords

Examples

			The ternary representations of 3, 9, and 11 are 10, 100, and 102.

Crossrefs

Cf. A007089, A081606.
Cf. A370916, A370917, A370919, A370920, A370921, A370922, A370923.

Programs

  • Mathematica
    Map[#[[1]] &, Select[Map[{#, #[[1]] > 0 && #[[1]] == #[[2]] &[{Length[
StringCases[#, "1"]], Length[StringCases[#, "10"]]}] &[
IntegerString[#, 3]]} &, Range[500]], #[[2]] &]]
  (* Peter J. C. Moses, Mar 05 2024 *)

A370919 Positive integers whose ternary representation includes at least one 1, and every 1 is followed by 2.

Original entry on oeis.org

5, 15, 17, 23, 45, 47, 50, 51, 53, 59, 69, 71, 77, 135, 137, 140, 141, 143, 150, 152, 153, 155, 158, 159, 161, 167, 177, 179, 185, 207, 209, 212, 213, 215, 221, 231, 233, 239, 405, 407, 410, 411, 413, 420, 422, 423, 425, 428, 429, 431, 450, 452, 455, 456
Offset: 1

Views

Author

Clark Kimberling, Mar 16 2024

Keywords

Examples

			The ternary representations of 5, 15, and 17 are 12, 120, and 122.

Crossrefs

Cf. A007089, A081606.
Cf. A370916, A370917, A370918, A370920, A370921, A370922, A370923.

Programs

  • Mathematica
    Map[#[[1]] &, Select[Map[{#, #[[1]] > 0 && #[[1]] == #[[2]] &[{Length[
StringCases[#, "1"]], Length[StringCases[#, "12"]]}] &[
IntegerString[#, 3]]} &, Range[500]], #[[2]] &]]   (* Peter J. C. Moses, Mar 05 2024 *)

A370920 Positive integers in whose ternary representation 2 occurs at least once, and every 2 is followed by 0.

Original entry on oeis.org

6, 15, 18, 19, 33, 42, 45, 46, 54, 55, 57, 58, 60, 87, 96, 99, 100, 114, 123, 126, 127, 135, 136, 138, 139, 141, 162, 163, 165, 166, 168, 171, 172, 174, 175, 177, 180, 181, 249, 258, 261, 262, 276, 285, 288, 289, 297, 298, 300, 301, 303, 330, 339, 342, 343
Offset: 1

Views

Author

Clark Kimberling, Mar 16 2024

Keywords

Crossrefs

Cf. A007089, A074940.
Cf. A370916, A370917, A370918, A370919, A370921, A370922, A370923.

Programs

  • Mathematica
    Map[#[[1]] &, Select[Map[{#, #[[1]] > 0 && #[[1]] == #[[2]] &[{Length[
StringCases[#, "2"]], Length[StringCases[#, "20"]]}] &[
IntegerString[#, 3]]} &, Range[500]], #[[2]] &]]   (* Peter J. C. Moses, Mar 05 2024 *)

Formula

The ternary representations of 6, 15, and 18 are 20, 120, and 200.

A370921 Positive integers in whose ternary representation, 2 occurs at least once, and every 2 is followed by 1.

Original entry on oeis.org

7, 16, 21, 22, 34, 43, 48, 49, 63, 64, 66, 67, 70, 88, 97, 102, 103, 115, 124, 129, 130, 144, 145, 147, 148, 151, 189, 190, 192, 193, 196, 198, 199, 201, 202, 205, 210, 211, 250, 259, 264, 265, 277, 286, 291, 292, 306, 307, 309, 310, 313, 331, 340, 345, 346
Offset: 1

Views

Author

Clark Kimberling, Mar 16 2024

Keywords

Examples

			The ternary representations of 7, 16, and 21 are 21, 121, and 210.

Crossrefs

Cf. A007089, A074940.
Cf. A370916, A370917, A370918, A370919, A370920, A370922, A370923.

Programs

  • Mathematica
    Map[#[[1]] &, Select[Map[{#, #[[1]] > 0 && #[[1]] == #[[2]] &[{Length[
StringCases[#, "2"]], Length[StringCases[#, "21"]]}] &[
IntegerString[#, 3]]} &, Range[500]], #[[2]] &]]
  (* Peter J. C. Moses, Mar 05 2024 *)
Showing 1-5 of 5 results.

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