cp's OEIS Frontend

A282151 Numbers n with k digits in base x (MSD(n)=d_k, LSD(n)=d_1) such that, chosen one of their digits in position d_k < j < d_1, is Sum_{i=j..k}{(i-j+1)*d_i} = Sum_{i=1..j-1}{(j-i)*d_i}. Case x = 10.

%I A282151 #13 May 30 2019 09:00:28
%S A282151 11,22,33,44,55,66,77,88,99,102,110,113,124,135,146,157,168,179,201,
%T A282151 204,215,220,226,237,248,259,306,311,317,328,330,339,402,408,419,421,
%U A282151 440,512,531,550,603,622,641,660,713,732,751,770,804,823,842,861,880,914,933
%N A282151 Numbers n with k digits in base x (MSD(n)=d_k, LSD(n)=d_1) such that, chosen one of their digits in position d_k < j < d_1, is Sum_{i=j..k}{(i-j+1)*d_i} = Sum_{i=1..j-1}{(j-i)*d_i}. Case x = 10.
%C A282151 All the palindromic numbers in base 10 with an even number of digits belong to the sequence.
%C A282151 Here the fulcrum is between two digits while in the sequence from A282107 to A282115 is one of the digits.
%H A282151 Paolo P. Lava, <a href="/A282151/b282151.txt">Table of n, a(n) for n = 1..10000</a>
%e A282151 If we split 2039 in 203 and 9 we have 3*1 + 0*2 + 2*3 = 9 for the left side and 9*1 = 9 for the right one.
%p A282151 P:=proc(n,h) local a,j,k: a:=convert(n, base, h):
%p A282151 for k from 1 to nops(a)-1 do
%p A282151 if add(a[j]*(k-j+1),j=1..k)=add(a[j]*(j-k),j=k+1..nops(a))
%p A282151 then RETURN(n); break: fi: od: end: seq(P(i,10),i=1..10^3);
%Y A282151 Cf. A282107 - A282115, A282143 - A282150.
%K A282151 nonn,base,easy
%O A282151 1,1
%A A282151 _Paolo P. Lava_, Feb 15 2017