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.

A365872 The "double commas" sequence, a variant of A121805. See the Comments and Example sections for detailed explanations.

Original entry on oeis.org

1, 25, 127, 271, 295, 403, 471, 499, 691, 725, 841, 877, 1019, 1201, 1223, 1285, 1387, 1529, 1711, 1733, 1795, 1897, 2041, 2065, 2169, 2353, 2417, 2561, 2585, 2689, 2873, 2937, 3083, 3149, 3335, 3441, 3467, 3613, 3679, 3865, 3971, 3997, 4145, 4253, 4321, 4349, 4537, 4685, 4793, 4861, 4889, 5079, 5269
Offset: 1

Views

Author

Eric Angelini and Giorgos Kalogeropoulos, Sep 21 2023

Keywords

Comments

The pair of digits adjacent to the comma between two terms forms an integer that is half the difference between the said terms. This is the lexicographically earliest sequence with this property. It will stop at some point, but when?

Examples

			a(1) = 1 and a(2) = 25 are separated by 24 units, and 24 is twice 12 (or 1,2);
a(2) = 25 and a(3) = 127 are separated by 102 units, and 102 is twice 51 (or 5,1);
a(3) = 127 and a(4) = 271 are separated by 144 units, and 144 is twice 72 (or 7,2);
a(4) = 271 and a(5) = 295 are separated by 24 units, and 24 is twice 12 (or 1,2); etc.

Links

Crossrefs

Cf. A121805 (the original 2006 sequence), A365873, A365874, A365875.

Programs

  • Mathematica
    a[1]=1;a[n_]:=a[n]=(k=a[n-1];While[2FromDigits@Join[{Mod[a[n-1],10]},{First@IntegerDigits@k}]!=k-a[n-1],k++];k);Array[a,70]

A365873 The "triple commas" sequence, a variant of A121805. See the Comments and Example sections for detailed explanations.

Original entry on oeis.org

1, 43, 136, 325, 487, 718, 985, 1138, 1381, 1414, 1537, 1750, 1753, 1846, 2032, 2098, 2344, 2470, 2476, 2662, 2728, 2974, 3103, 3202, 3271, 3310, 3319, 3598, 3847, 4069, 4351, 4393, 4495, 4657, 4879, 5164, 5299, 5584, 5719, 6007, 6235, 6403, 6511, 6559, 6847, 7078, 7339, 7630, 7651, 7702, 7783, 7894
Offset: 1

Views

Author

Eric Angelini and Giorgos Kalogeropoulos, Sep 21 2023

Keywords

Comments

The pair of digits adjacent to the comma between two terms forms an integer that is the third of the difference between the said terms. This is the lexicographically earliest sequence with this property. It will stop at some point, but when?

Examples

			a(1) = 1 and a(2) = 43 are separated by 42 units, and 42 is 3*14 (or 1,4);
a(2) = 43 and a(3) = 136 are separated by 93 units, and 93 is 3*31 (or 3,1);
a(3) = 136 and a(4) = 325 are separated by 189 units, and 189 is 3*63 (or 6,3);
a(4) = 325 and a(5) = 487 are separated by 162 units, and 162 is 3*54 (or 5,4); etc.

Links

Crossrefs

Cf. A121805 (the original 2006 sequence), A365872, A365874, A365875.

Programs

  • Mathematica
    a[1]=1;a[n_]:=a[n]=(k=a[n-1];While[3FromDigits@Join[{Mod[a[n-1],10]},{First@IntegerDigits@k}]!=k-a[n-1],k++];k);Array[a,70]

A365874 The "quadruple commas" sequence, a variant of A121805. See the Comments and Example sections for detailed explanations.

Original entry on oeis.org

1, 65, 273, 409, 797, 1081, 1125, 1329, 1693, 1817, 2105, 2313, 2441, 2489, 2857, 3149, 3521, 3573, 3705, 3917, 4213, 4349, 4725, 4941, 4997, 5297, 5597, 5897, 6201, 6265, 6489, 6873, 7021, 7089, 7477, 7785, 8017, 8329, 8721, 8793, 8945, 9181, 9257, 9573, 9729, 10093, 10217, 10501, 10545, 10749, 11113
Offset: 1

Views

Author

Eric Angelini and Giorgos Kalogeropoulos, Sep 21 2023

Keywords

Comments

The pair of digits adjacent to the comma between two terms forms an integer that is the fourth of the difference between the said terms. This is the lexicographically earliest sequence with this property. It will stop at some point, but when?

Examples

			a(1) = 1 and a(2) = 65 are separated by 64 units, and 64 is 4*16 (or 1,6);
a(2) = 65 and a(3) = 273 are separated by 208 units, and 208 is 4*52 (or 5,2);
a(3) = 273 and a(4) = 409 are separated by 136 units, and 136 is 4*34 (or 3,4);
a(4) = 409 and a(5) = 797 are separated by 388 units, and 388 is 4*97 (or 9,7); etc.

Links

Crossrefs

Cf. A121805 (the original 2006 sequence), A365872, A365873, A365875.

Programs

  • Mathematica
    a[1]=1;a[n_]:=a[n]=(k=a[n-1];While[4FromDigits@Join[{Mod[a[n-1],10]},{First@IntegerDigits@k}]!=k-a[n-1],k++];k);Array[a,70]
Showing 1-3 of 3 results.

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