cp's OEIS Frontend

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

%I A365875 #11 Sep 25 2023 10:59:26
%S A365875 1,92,104,118,136,152,164,178,206,232,254,278,316,352,384,428,476,532,
%T A365875 584,648,726,812,904,998,1016,1032,1044,1058,1076,1092,1104,1118,1136,
%U A365875 1152,1164,1178,1196,1212,1224,1238,1256,1272,1284,1298,1316,1332,1344,1358,1376,1392,1404,1418,1436,1452,1464
%N A365875 The "reversed commas" sequence, a variant of A121805. See the Comments and Example sections for detailed explanations.
%C A365875 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.
%H A365875 Eric Angelini, <a href="https://cinquantesignes.blogspot.com/2023/09/commas-variants.html">Commas variants</a>, personal blog, Sept 2023.
%e A365875 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.
%e A365875 a(1) = 1 and a(2) = 92 are separated by 91 units, and 91 is 19 backwards (or 1,9);
%e A365875 a(2) = 92 and a(3) = 104 are separated by 12 units, and 12 is 21 backwards (or 2,1);
%e A365875 a(3) = 104 and a(4) = 118 are separated by 14 units, and 14 is 41 backwards (or 4,1);
%e A365875 a(4) = 118 and a(5) = 136 are separated by 18 units, and 18 is 81 backwards (or 8,1); etc.
%e A365875 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.
%t A365875 NestList[(s=#;li=First@*IntegerDigits/@Table[s+10*k+Mod[s,10],{k,9}]-Range@9;
%t A365875 Last@Table[s+FromDigits@Join[Position[li,0][[c]],{Mod[s,10]}],{c,Length@Position[li,0]}])&,1,2513]
%Y A365875 Cf. A121805 (the original 2006 sequence), A365872, A365873, A365874.
%K A365875 base,nonn,fini
%O A365875 1,2
%A A365875 _Eric Angelini_ and _Giorgos Kalogeropoulos_, Sep 21 2023