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%I #8 May 30 2019 09:00:14
%S 9,18,27,36,45,54,63,66,72,75,84,93,102,111,129,132,141,144,150,159,
%T 198,201,207,216,258,273,288,330,345,360,387,402,417,432,459,474,489,
%U 504,513,515,524,528,533,542,551,576,581,585,590,599,600,642,647,657,672
%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 = 8.
%C All the palindromic numbers in base 8 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.
%C The first number with this property in all the bases from 2 to 8 is
%C 10296444436. - _Giovanni Resta_, Feb 16 2017
%H Paolo P. Lava, <a href="/A282149/b282149.txt">Table of n, a(n) for n = 1..10000</a>
%e 672 in base 8 is 1240. If we split the number in 12 and 40 we have 2*1 + 1*2 = 4 for the left side and 4*1 + 0*2 = 4 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,8),i=1..10^3);
%Y Cf. A282107 - A282115, A282143 - A282148, A282150, A282151.
%K nonn,base,easy
%O 1,1
%A _Paolo P. Lava_, Feb 15 2017
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