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A282146 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 = 5.

%I A282146 #7 May 30 2019 08:59:51
%S A282146 6,12,18,24,27,30,33,39,51,54,60,81,90,102,111,120,126,128,134,135,
%T A282146 150,156,165,177,186,195,207,216,228,237,246,252,255,261,270,282,291,
%U A282146 300,303,312,321,333,342,354,363,372,376,378,387,396,405,408,417,429,438,447
%N A282146 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 = 5.
%C A282146 All the palindromic numbers in base 5 with an even number of digits belong to the sequence.
%C A282146 Here the fulcrum is between two digits while in the sequence from A282107 to A282115 is one of the digits.
%C A282146 Numbers with this property in all the bases from 2 to 5 are: 3120, 9615, 10366, 16610, 17812, 22129, 33329, 100726, 163800, 202039, 208172, 212636, 258221, 270337, 298575, 420240, 462608, 475782, 492420, 523679, 549537, 550200, 587842, 594511, 610273, 655350, 671844, 675872, 681280, 730161, 738480, 840798, 842614, 848655, 855973, 925515, 987751, ...
%H A282146 Paolo P. Lava, <a href="/A282146/b282146.txt">Table of n, a(n) for n = 1..10000</a>
%e A282146 447 in base 5 is 3242. If we split the number in 32 and 42 we have 2*1 + 3*2 = 8 for the left side and 4*1 + 2*2 = 8 for the right one.
%p A282146 P:=proc(n,h) local a,j,k: a:=convert(n, base, h):
%p A282146 for k from 1 to nops(a)-1 do
%p A282146 if add(a[j]*(k-j+1),j=1..k)=add(a[j]*(j-k),j=k+1..nops(a))
%p A282146 then RETURN(n); break: fi: od: end: seq(P(i,5),i=1..10^3);
%Y A282146 Cf. A282107 - A282115, A282143 - A282145, A282147 - A282151.
%K A282146 nonn,base,easy
%O A282146 1,1
%A A282146 _Paolo P. Lava_, _Giovanni Resta_, Feb 07 2017