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 A373117 #17 Apr 13 2025 19:56:25 %S A373117 0,1,2,3,4,5,6,7,8,9,10,11,20,22,30,33,40,44,50,55,60,66,70,77,80,88, %T A373117 90,99,100,101,102,110,111,113,121,124,131,135,141,146,151,157,161, %U A373117 168,171,179,181,191,200,201,202,204,212,215,220,222,226,232,237,242,248,252,259,262,272,282,292,300,303,306,311 %N A373117 Stable numbers on vertical blade (see the Example section for an explanation). %H A373117 Eric Angelini, <a href="https://cinquantesignes.blogspot.com/2024/05/balanced-numbers-no-palindromes.html">Balanced numbers</a>, personal blog, May 2024. %H A373117 Hans Havermann, <a href="http://chesswanks.com/seq/b373117.txt">10000-term b-file</a>. %e A373117 We place the k digits of a number in succession in k adjacent square boxes forming a rectangle of base k and height 1. We can only place a vertical blade under this rectangle in two ways: exactly between two boxes [positions (a) and (d) below] or exactly under the middle of a box [position (b) and (c) below]. %e A373117 If the blade is placed in position (a) between the two 1s of 11, the number 11 is stable. %e A373117 If the blade is placed in (b) exactly under the 0 of 101, the number 101 is stable. %e A373117 If the blade is placed in (c) exactly under the 1 of 10, the number is stable. %e A373117 If the blade is placed in (d) between the 0 and the 2 of 102, the number 102 is stable. %e A373117 For the last two examples, the balance of the number considered can be explained as follows: the distance which separates a digit from the blade comes into play - the more this distance increases, the heavier the digit in question is. So, the digit 1 of 102 weighs 2 in reality (weight*distance = 1*2 = 2). This quantity balances the influence of the 2 of 102 (for which weight*distance = 2*1 = 2 too). %e A373117 . %e A373117 .+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ %e A373117 .| | | | | | | | | | | | | | | | %e A373117 .+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ %e A373117 .| | 1 | 1 | | 1 | 0 | 1 | | 1 | 0 | | 1 | 0 | 2 | | %e A373117 .+---+---a---+---+---+-b-+---+---+-c-+---+---+---+---d---+---+ %e A373117 .| | | | | | | | | | | | | | | | %e A373117 .+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ %e A373117 . %Y A373117 Cf. A282115, A282151. %K A373117 base,nonn %O A373117 1,3 %A A373117 _Eric Angelini_ and _Giorgos Kalogeropoulos_, May 25 2024