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A282115 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 = 10. 18

%I

%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 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 = 10.

%C All the palindromic numbers in base 10 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.

%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 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,10),i=1..10^3);

%Y Cf. A282107 - A282114.

%K nonn,base,easy

%O 1,1

%A _Paolo P. Lava_, Feb 06 2017

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Last modified October 17 13:30 EDT 2021. Contains 348049 sequences. (Running on oeis4.)