A365872 - OEIS

%I #8 Sep 25 2023 08:52:34

%S 1,25,127,271,295,403,471,499,691,725,841,877,1019,1201,1223,1285,

%T 1387,1529,1711,1733,1795,1897,2041,2065,2169,2353,2417,2561,2585,

%U 2689,2873,2937,3083,3149,3335,3441,3467,3613,3679,3865,3971,3997,4145,4253,4321,4349,4537,4685,4793,4861,4889,5079,5269

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

%C The pair of digits adjacent to the comma between two terms forms an integer that is half the difference between the said terms. This is the lexicographically earliest sequence with this property. It will stop at some point, but when?

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

%e a(1) = 1 and a(2) = 25 are separated by 24 units, and 24 is twice 12 (or 1,2);

%e a(2) = 25 and a(3) = 127 are separated by 102 units, and 102 is twice 51 (or 5,1);

%e a(3) = 127 and a(4) = 271 are separated by 144 units, and 144 is twice 72 (or 7,2);

%e a(4) = 271 and a(5) = 295 are separated by 24 units, and 24 is twice 12 (or 1,2); etc.

%t a[1]=1;a[n_]:=a[n]=(k=a[n-1];While[2FromDigits@Join[{Mod[a[n-1],10]},{First@IntegerDigits@k}]!=k-a[n-1],k++];k);Array[a,70]

%Y Cf. A121805 (the original 2006 sequence), A365873, A365874, A365875.

%K base,nonn,fini

%O 1,2

%A _Eric Angelini_ and _Giorgos Kalogeropoulos_, Sep 21 2023