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

1,2

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?

Links

Table of n, a(n) for n=1..53.

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

Example

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.

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]

Crossrefs

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

Sequence in context: A042216 A042218 A045166 * A232873 A232856 A232792

Adjacent sequences: A365869 A365870 A365871 * A365873 A365874 A365875

Keyword

base,nonn,fini

Author

Eric Angelini and Giorgos Kalogeropoulos, Sep 21 2023

Status

approved