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%I #13 May 30 2019 08:59:11
%S 50,57,64,71,78,85,92,100,107,114,121,128,135,142,150,157,164,171,178,
%T 185,192,200,207,214,221,228,235,242,250,257,264,271,278,285,292,300,
%U 307,314,321,328,335,342,345,350,352,359,366,373,380,387,395,399,402,409
%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 = 7.
%C All the palindromic numbers in base 7 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 7 are: 53060873, 55161152, 151009636, 343518281, 505587488, 513015908, ...- _Giovanni Resta_, Feb 13 2017
%H Paolo P. Lava, <a href="/A282112/b282112.txt">Table of n, a(n) for n = 1..10000</a>
%e 409 in base 7 is 1123. If j = 2 (digit 2) we have 1*1 + 1*2 = 3 for the left side and 3*1 = 3 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,7),i=1..10^3);
%Y Cf. A282107 - A282111, A282113 - A282115.
%K nonn,base,easy
%O 1,1
%A _Paolo P. Lava_, Feb 06 2017
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