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 A387069 #21 Aug 24 2025 11:33:29
%S A387069 10,12,273,546,582,11808655,34503520,35555155,54813136653716,
%T A387069 1066338805156287287067,1124161332414632881704,2305867155177711644802,
%U A387069 2306166776784312535170,5744341611556736174883,2705154287309969771123575182312
%N A387069 Numbers whose representation in base b are their representation in base b+1 with a "0" added at the end for some b.
%C A387069 The corresponding b's are: 2, 2, 3, 3, 3, 5, 5, 5, 7, 9, 9, 9, 9, 9, 11, ...
%C A387069 From _Sean A. Irvine_, Aug 18 2025: (Start)
%C A387069 Numbers k such that k = Sum_{j>=1} d(j) * b^j = Sum_{j>=0} d(j+1) * (b+1)^j where 0 <= d(j) < b.
%C A387069 For k to be a solution in base b, we require Sum d(j) = 0 (mod b) and Sum_{j>=2} (-1)^j*d(j) = 2*d(1) (mod b+1). (End)
%H A387069 Sean A. Irvine, <a href="/A387069/a387069.py.txt">Python program</a>
%e A387069 a(1) = 10, is 1010 in base 2 and 101 in base 3.
%e A387069 a(2) = 12, is 1100 in base 2 and 110 in base 3.
%e A387069 a(3) = 273, is 101010 in base 3 and 10101 in base 4.
%o A387069 (PARI) isok(k) = for (b=2, k-1, if (digits(k, b) == concat(digits(k, b+1), 0), return(b));); \\ _Michel Marcus_, Aug 16 2025
%Y A387069 Cf. A062845, A062853, A062928.
%K A387069 nonn,base,more,new
%O A387069 1,1
%A A387069 _Cristiano Campos de Oliveira_, Aug 15 2025
%E A387069 a(9)-a(15) from _Sean A. Irvine_, Aug 18 2025