A365874 - OEIS

A365874

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

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

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OFFSET

1,2

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?

LINKS

Table of n, a(n) for n=1..51.

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

EXAMPLE

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.

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]

CROSSREFS

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