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

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

1,2

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?

Links

Table of n, a(n) for n=1..52.

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

Example

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.

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]

Crossrefs

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

Sequence in context: A142311 A069757 A354671 * A142394 A086760 A142412

Adjacent sequences: A365870 A365871 A365872 * A365874 A365875 A365876

Keyword

base,nonn,fini

Author

Eric Angelini and Giorgos Kalogeropoulos, Sep 21 2023

Status

approved