A365875 The "reversed commas" sequence, a variant of A121805. See the Comments and Example sections for detailed explanations.

1, 92, 104, 118, 136, 152, 164, 178, 206, 232, 254, 278, 316, 352, 384, 428, 476, 532, 584, 648, 726, 812, 904, 998, 1016, 1032, 1044, 1058, 1076, 1092, 1104, 1118, 1136, 1152, 1164, 1178, 1196, 1212, 1224, 1238, 1256, 1272, 1284, 1298, 1316, 1332, 1344, 1358, 1376, 1392, 1404, 1418, 1436, 1452, 1464

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 the difference between the said terms, but read backwards. This is the lexicographically earliest sequence with this property, provide the largest next term is always chosen when there is a choice. The sequence ends after 2514 steps with a(2514) = 99952.

Examples

			After a(1) = 1, we have multiple choices for a(2); they are 12, 22, 32, 42, 52, 62, 72, 82 and 92. We keep 92 for a(2) as 92 is the largest term.
a(1) = 1 and a(2) = 92 are separated by 91 units, and 91 is 19 backwards (or 1,9);
a(2) = 92 and a(3) = 104 are separated by 12 units, and 12 is 21 backwards (or 2,1);
a(3) = 104 and a(4) = 118 are separated by 14 units, and 14 is 41 backwards (or 4,1);
a(4) = 118 and a(5) = 136 are separated by 18 units, and 18 is 81 backwards (or 8,1); etc.
The next choices we encountered (keeping the largest term) were after a(8) = 178 -> {196,206}, then after 812 -> {894,904}, 1976 -> {1992,2002}, 3956 -> {3992,4002}, 19984 -> {19998,20008}, 39958 -> {39996,40006}, 49952 -> {49994,50004}, etc.
		

Links

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

Crossrefs

Cf. A121805 (the original 2006 sequence), A365872, A365873, A365874.

Programs

Mathematica

NestList[(s=#;li=First@*IntegerDigits/@Table[s+10*k+Mod[s,10],{k,9}]-Range@9;
Last@Table[s+FromDigits@Join[Position[li,0][[c]],{Mod[s,10]}],{c,Length@Position[li,0]}])&,1,2513]