cp's OEIS Frontend

A282145 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 = 4.

%I A282145 #7 May 30 2019 08:59:46
%S A282145 5,10,15,18,20,23,33,40,53,60,65,67,72,80,85,92,98,105,118,125,130,
%T A282145 132,137,150,157,160,163,170,183,190,193,195,202,212,215,222,235,240,
%U A282145 255,260,261,268,274,281,288,294,301,307,314,320,321,326,333,339,340,346
%N A282145 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 = 4.
%C A282145 All the palindromic numbers in base 4 with an even number of digits belong to the sequence.
%C A282145 Here the fulcrum is between two digits while in the sequence from A282107 to A282115 is one of the digits.
%H A282145 Paolo P. Lava, <a href="/A282145/b282145.txt">Table of n, a(n) for n = 1..10000</a>
%e A282145 222 in base 4 is 3132. If we split the number in 31 and 32 we have 1*1 + 3*2 = 7 for the left side and 3*1 + 2*2 = 7 for the right one.
%p A282145 P:=proc(n,h) local a,j,k: a:=convert(n, base, h):
%p A282145 for k from 1 to nops(a)-1 do
%p A282145 if add(a[j]*(k-j+1),j=1..k)=add(a[j]*(j-k),j=k+1..nops(a))
%p A282145 then RETURN(n); break: fi: od: end: seq(P(i,4),i=1..10^3);
%Y A282145 Cf. A282107 - A282115, A282143, A282144, A282146 - A282151.
%K A282145 nonn,base,easy
%O A282145 1,1
%A A282145 _Paolo P. Lava_, _Giovanni Resta_, Feb 07 2017