cp's OEIS Frontend

A282110 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 = 5.

%I A282110 #13 May 30 2019 08:58:59
%S A282110 26,31,36,41,46,52,57,62,67,72,78,83,88,93,98,104,109,114,119,124,127,
%T A282110 130,132,137,142,147,153,155,158,163,168,173,179,180,184,189,194,199,
%U A282110 205,230,251,254,259,260,264,269,274,276,285,301,310,326,335,351,360,381
%N A282110 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 = 5.
%C A282110 All the palindromic numbers in base 5 with an odd number of digits belong to the sequence.
%C A282110 Here the fulcrum is one of the digits while in the sequence from A282143 to A282151 is between two digits.
%C A282110 Numbers with this property in all the bases from 2 to 5 are: 78, 650, 1550, 4368, 4433, 4805, 6913, 7410, 16709, 31824, 35175, 41216, 104272, 107584, 132285, 144781, 165059, 173305, 174096, 190468, 195473, 201900, 205005, 205261, 214432, 231521, 243984, 275026, 278528, 295275, 304562, 313769, ...
%H A282110 Paolo P. Lava, <a href="/A282110/b282110.txt">Table of n, a(n) for n = 1..10000</a>
%e A282110 137 in base 5 is 1022. If j=2 (the second 2 from right) we have 0*1 + 1*2 = 2 for the left side and 2*1 = 2 for the right one.
%p A282110 P:=proc(n,h) local a,j,k: a:=convert(n, base, h):
%p A282110 for k from 1 to nops(a)-1 do
%p A282110 if add(a[j]*(k-j),j=1..k)=add(a[j]*(j-k),j=k+1..nops(a)) then
%p A282110 RETURN(n); break: fi: od: end: seq(P(i,5),i=1..10^3);
%Y A282110 CF. A282107 - A282109, A282111 - A282115.
%K A282110 base,nonn,easy
%O A282110 1,1
%A A282110 _Paolo P. Lava_, Feb 06 2017