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 A138141 #25 Feb 15 2024 08:45:21
%S A138141 1,2,3,4,5,6,7,8,9,12,23,34,45,56,67,78,89,123,234,345,456,567,678,
%T A138141 789,1234,2345,3456,4567,5678,6789,12345,23456,34567,45678,56789,
%U A138141 123456,234567,345678,456789,1234567,2345678,3456789,12345678,23456789,123456789
%N A138141 Numbers with digits in ascending order that differ exactly by 1.
%C A138141 This finite sequence has 45 members. The last member is 123456789. There are 10-k members with k digits. See A052017 for primes in this sequence. All members with 3 or more digits are straight-line numbers A135643.
%F A138141 a(n) = floor(((9*t^2 - 189*t + 18*n + 182) * (10^t - 1) - 18*t) / 162), where t = floor((21 - sqrt(369 - 8*n)) / 2). - _Christopher J. Thomas_, Feb 14 2024
%t A138141 Table[FromDigits/@Partition[Range[9],n,1],{n,9}]//Flatten (* _Harvey P. Dale_, Mar 19 2017 *)
%Y A138141 Cf. A052017, A059043, A135643, A138142.
%K A138141 base,easy,fini,full,nonn
%O A138141 1,2
%A A138141 _Omar E. Pol_, Mar 19 2008