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%I #12 May 30 2019 08:59:17
%S 65,73,81,89,97,105,113,121,130,138,146,154,162,170,178,186,195,203,
%T 211,219,227,235,243,251,260,268,276,284,292,300,308,316,325,333,341,
%U 349,357,365,373,381,390,398,406,414,422,430,438,446,455,463,471,479,487,495
%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+1..k}{(i-j)*d_i} = Sum_{i=1..j-1}{(j-i)*d_i}. Case x = 8.
%C All the palindromic numbers in base 8 with an odd number of digits belong to the sequence.
%C Here the fulcrum is one of the digits while in the sequence from A282143 to A282151 is between two digits.
%C Numbers with this property in all the bases from 2 to 8 are: 2438269535, 6936679443, 8657968788, 11107027008, 21733512704, ... - _Giovanni Resta_, Feb 13 2017
%H Paolo P. Lava, <a href="/A282113/b282113.txt">Table of n, a(n) for n = 1..10000</a>
%e 1084 in base 8 is 2074. If j = 2 (digit 7) we have 0*1 + 2*2 = 4 for the left side and 4*1 = 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),j=1..k)=add(a[j]*(j-k),j=k+1..nops(a)) then
%p RETURN(n); break:fi: od: end: seq(P(i,8),i=1..10^3);
%Y Cf. A282107 - A282112, A282114, A282115.
%K nonn,base,easy
%O 1,1
%A _Paolo P. Lava_, Feb 06 2017
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