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

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

Author

Eric Angelini and Giorgos Kalogeropoulos, Sep 21 2023

Keywords

• base
• nonn
• fini

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

• Eric Angelini, Commas variants, personal blog, Sept 2023.

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]