proposed

approved

editing

proposed

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]

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editing

proposed

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, 8038, 8302, 8386, 8590, 8614, 8758, 9025, 9202, 9289, 9586, 9793, 9910, 9937, 10150, 10153, 10246, 10429, 10702

1, 43, 136, 325, 487,

allocated The "triple commas" sequence, a variant of A121805. See the Comments and Example sections for Eric Angelinidetailed 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, 8038, 8302, 8386, 8590, 8614, 8758, 9025, 9202, 9289, 9586, 9793, 9910, 9937, 10150, 10153, 10246, 10429, 10702

1,2

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?

Eric Angelini, <a href="https://cinquantesignes.blogspot.com/2023/09/commas-variants.html">Commas variants</a>, personal blog, Sept 2023.

1, 43, 136, 325, 487,

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.

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

allocated

base,nonn,fini

Eric Angelini and Giorgos Kalogeropoulos, Sep 21 2023

approved

editing

allocated for Eric Angelini

allocated

approved