This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A365221 #15 Dec 21 2024 18:06:50 %S A365221 1,9,11,99,101,909,2,8,22,88,3,7,33,77,4,6,44,66,5,55,505,515,191,111, %T A365221 292,121,181,131,171,141,161,151,252,262,242,272,232,282,222,383,323, %U A365221 393,212,494,313,595,333,373,343,363,353,454,464,444,474,434,484,424,606,404,616,414,626,4004,636,4014,646,4024 %N A365221 Each term is a "Go flat integer" (GFI), but a(n) + a(n+1) is always a "Go down integer" (GDI). More details in the Comments section. %C A365221 The rightmost digit R of a GDI is always smaller than the leftmost digit L of the same GDI. The first such integer is 10, as we need at least two digits for a sound GDI. When R = L we have a "Go flat integer", or GFI. We admit that 0 is the first GFI (followed by 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, 121, etc.) This sequence is the lexicographically earliest of distinct nonnegative terms with this property, starting with a(1) = 1. %H A365221 Eric Angelini, <a href="http://cinquantesignes.blogspot.com/2023/08/go-down-go-up-go-flat-integers.html">Go down, go up, go flat integers</a>, Personal blog "Cinquante signes", Aug 2023. %H A365221 Eric Angelini, <a href="/A365217/a365217.pdf">Go down, go up, go flat integers</a>, Personal blog "Cinquante signes", Aug 2023. [Cached copy] %e A365221 a(1) + a(2) = 1 + 9 = 10 and 10 is a GDI; a(2) + a(3) = 9 + 11 = 20 and 20 is a GDI;a(3) + a(4) = 11 + 99 = 110 and 110 is a GDI;a(4) + a(5) = 99 + 101 = 200 and 200 is a GDI;a(5) + a(6) = 101 + 909 = 1010 and 1010 is a GDI; etc. %t A365221 a[1]=1;a[n_]:=a[n]=(k=1;While[Last[i=IntegerDigits@k]!=First@i ||MemberQ[Array[a,n-1],k]||First[i1=IntegerDigits[a[n-1]+k]]<=Last@i1,k++];k);Array[a,100] (* _Giorgos Kalogeropoulos_, Aug 27 2023 *) %Y A365221 Cf. A365217, A365219, A365220. %K A365221 base,nonn %O A365221 1,2 %A A365221 _Eric Angelini_, Aug 26 2023 %E A365221 Data corrected by _Giorgos Kalogeropoulos_