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 A282107 #11 May 30 2019 08:58:41
%S A282107 5,7,10,14,17,20,21,27,28,31,34,35,39,40,42,49,54,56,57,62,65,68,70,
%T A282107 73,78,80,84,85,93,98,99,107,108,112,114,119,124,127,130,133,136,140,
%U A282107 141,146,147,155,156,160,161,167,168,170,175,177,186,196,198,201,214
%N A282107 Numbers n with k digits in base x (MSD(n)_x=d_k, LSD(n)_x=d_1) such that, chosen one of their digits in position d_k < j < d_1, is Sum_{i=j+1..k}{(i-j)*d_i} = Sum_{i=1..j-1}{(j-i)*d_i}. Case x = 2.
%C A282107 All the palindromic numbers in base 2 with an odd number of digits belong to the sequence.
%C A282107 Here the fulcrum is one of the digits while in the sequence from A282143 to A282151 is between two digits.
%H A282107 Paolo P. Lava, <a href="/A282107/b282107.txt">Table of n, a(n) for n = 1..10000</a>
%e A282107 897 in base 2 is 1110000001. If j = 7 (the first 0 from left) we have 1*1 + 1*2 + 1*3 = 6 for the left side and 0*1 + 0*2 + 0*3 + 0*4 + 0*5 + 1*6 = 6 for the right one.
%p A282107 P:=proc(n,h) local a,j,k: a:=convert(n, base, h):
%p A282107 for k from 1 to nops(a)-1 do
%p A282107 if add(a[j]*(k-j),j=1..k)=add(a[j]*(j-k),j=k+1..nops(a))
%p A282107 then RETURN(n); break: fi: od: end: seq(P(i,2),i=1..10^3);
%Y A282107 Cf. A282108 - A282115.
%K A282107 nonn,base,easy
%O A282107 1,1
%A A282107 _Paolo P. Lava_, Feb 06 2017