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%I #15 Aug 22 2023 11:58:07
%S 101,111,121,131,141,151,161,171,181,191,202,212,222,232,242,252,262,
%T 272,282,292,303,313,323,333,343,353,363,373,383,393,404,414,424,434,
%U 444,454,464,474,484,494,505,515,525,535,545,555,565,575,585,595,606,616,626
%N Numbers m with k digits in base b (MSD(m)=d_k, LSD(m)=d_1) such that, for one of their digits in position d_k < j < d_1, Sum_{i=j+1..k} (i-j)*d_i = Sum_{i=1..j-1} (j-i)*d_i. Case b = 10.
%C All the numbers that are palindromic in base 10 and have an odd number of digits belong to this sequence.
%C Here the fulcrum is one of the digits while in the sequences from A282143 to A282151 it is between two digits.
%H Paolo P. Lava, <a href="/A282115/b282115.txt">Table of n, a(n) for n = 1..10000</a>
%e 10467: if j = 2 (digit 6) we have 4*1 + 0*2 + 1*3 = 7 for the left side and 7*1 = 7 for the right side.
%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),j=1..k)=add(a[j]*(j-k),j=k+1..nops(a)) then
%p RETURN(n); break: fi: od: end: seq(P(i,10),i=1..10^3);
%Y Cf. A282107, A282108, A282109, A282110, A282111, A282112, A282113, A282114.
%K nonn,base,easy
%O 1,1
%A _Paolo P. Lava_, Feb 06 2017
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