Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #11 May 30 2019 08:58:52
%S 17,21,25,29,34,38,42,46,51,55,59,63,66,68,70,74,78,83,84,87,91,95,
%T 100,116,129,136,145,152,161,168,177,184,197,204,213,220,229,236,245,
%U 252,257,259,263,264,267,271,272,273,280,289,296,305,312,325,332,336,341
%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 = 4.
%C All the palindromic numbers in base 4 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="/A282109/b282109.txt">Table of n, a(n) for n = 1..10000</a>
%e 83 in base 4 is 1103. If j = 2 (digit 0) 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,4),i=1..10^3);
%Y A282107, A282108, A282110 - A282115.
%K base,nonn,easy
%O 1,1
%A _Paolo P. Lava_, Feb 06 2017