cp's OEIS Frontend

A282109 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+1..k}{(i-j)*d_i} = Sum_{i=1..j-1}{(j-i)*d_i}. Case x = 4.

%I A282109 #11 May 30 2019 08:58:52
%S A282109 17,21,25,29,34,38,42,46,51,55,59,63,66,68,70,74,78,83,84,87,91,95,
%T A282109 100,116,129,136,145,152,161,168,177,184,197,204,213,220,229,236,245,
%U A282109 252,257,259,263,264,267,271,272,273,280,289,296,305,312,325,332,336,341
%N A282109 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+1..k}{(i-j)*d_i} = Sum_{i=1..j-1}{(j-i)*d_i}. Case x = 4.
%C A282109 All the palindromic numbers in base 4 with an odd number of digits belong to the sequence.
%C A282109 Here the fulcrum is one of the digits while in the sequence from A282143 to A282151 is between two digits.
%H A282109 Paolo P. Lava, <a href="/A282109/b282109.txt">Table of n, a(n) for n = 1..10000</a>
%e A282109 83 in base 4 is 1103. If j = 2 (digit 0) we have 1*1 + 1*2 = 3 for the left side and 3*1 = 3 for the right one.
%p A282109 P:=proc(n,h) local a,j,k: a:=convert(n, base, h):
%p A282109 for k from 1 to nops(a)-1 do
%p A282109 if add(a[j]*(k-j),j=1..k)=add(a[j]*(j-k),j=k+1..nops(a)) then
%p A282109 RETURN(n); break: fi: od: end: seq(P(i,4),i=1..10^3);
%Y A282109 A282107, A282108, A282110 - A282115.
%K A282109 base,nonn,easy
%O A282109 1,1
%A A282109 _Paolo P. Lava_, Feb 06 2017