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 A325114 #44 Sep 28 2024 07:10:36
%S A325114 1,2,3,4,5,6,8,9,10,11,12,13,15,16,18,19,20,22,23,24,25,26,29,30,31,
%T A325114 32,33,34,36,38,39,40,41,43,44,45,46,48,50,51,52,53,54,55,58,59,60,61,
%U A325114 62,64,65,66,68,69,80,81,82,83,85,86,88,89,90,92,93,94,95,96,99,100,101,102,103,104,106,108,109,110,111,113,115,116,118,120
%N A325114 Integers k such that no nonzero subsequence of the decimal representation of k is divisible by 7.
%C A325114 Does not contain 114 (helps to distinguish this from related sequences).
%C A325114 From _David A. Corneth_, Sep 10 2024: (Start)
%C A325114 Any term greater than 10^6 must have a digit 0. Proof: Any term between 10^6 and 10^7 has a 0.
%C A325114 Proof via induction and contradiction; any 7 digital number term has a digit 0. Suppose some number with k with q > 7 digits has no digit 0. Then floor(k/10) is a term and has no digit 0 and q - 1 digits. But there is no such number. A contradiction. Therefore any term with at least 7 digits has a digit 0. (End)
%H A325114 David A. Corneth, <a href="/A325114/b325114.txt">Table of n, a(n) for n = 1..10000</a>
%H A325114 David A. Corneth, <a href="/A325114/a325114.gp.txt">PARI program</a>
%t A325114 With[{k = 7}, Select[Range@ 100, NoneTrue[DeleteCases[FromDigits /@ Rest@ Subsequences[IntegerDigits@ #], 0], Mod[#, k] == 0 &] &]] (* _Michael De Vlieger_, Mar 31 2019 *)
%o A325114 (PARI) \\ See Corneth link
%Y A325114 Cf. A014261 (for 2), A325112 (for 3), A325113 (for 4), A261189 (for 5).
%Y A325114 See A376046 for complement.
%K A325114 nonn,base
%O A325114 1,2
%A A325114 _Jonathan Kal-El Peréz_, Mar 27 2019
%E A325114 More than the usual number of terms are shown in order to distinguish this from a new sequence arising from the game of "buzz" (cf. A092433). - _N. J. A. Sloane_, Sep 09 2024