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%I #8 May 30 2019 08:59:34
%S 3,6,9,12,15,18,19,24,25,30,33,36,38,45,48,50,51,60,63,66,69,72,75,76,
%T 81,87,90,96,100,102,105,117,120,126,129,131,132,138,143,144,150,152,
%U 153,162,165,174,179,180,189,192,193,195,200,204,205,210,219,231,234
%N 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 = 2.
%C All the palindromic numbers in base 2 with an even number of digits belong to the sequence.
%C Here the fulcrum is between two digits while in the sequence from A282107 to A282115 is one of the digits.
%H Paolo P. Lava, <a href="/A282143/b282143.txt">Table of n, a(n) for n = 1..10000</a>
%e 143 in base 2 is 10001111. If we split the number in 10001 and 111 we have 1*1 + 0*2 + 0*3 + 0*4 + 1*5 = 6 for the left side and 1*1 + 1*2 + 1*3 = 6 for the right one.
%p P:=proc(n,h) local a,j,k: a:=convert(n, base, h):
%p for k from 1 to nops(a)-1 do
%p if add(a[j]*(k-j+1),j=1..k)=add(a[j]*(j-k),j=k+1..nops(a))
%p then RETURN(n); break: fi: od: end: seq(P(i,2),i=1..10^3);
%Y Cf. A282107 - A282115, A282144 - A282151.
%K nonn,base,easy
%O 1,1
%A _Paolo P. Lava_, _Giovanni Resta_, Feb 07 2017
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