cp's OEIS Frontend

A282147 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..k}{(i-j+1)*d_i} = Sum_{i=1..j-1}{(j-i)*d_i}. Case x = 6.

%I A282147 #8 May 30 2019 09:00:00
%S A282147 7,14,21,28,35,38,42,45,52,59,73,76,83,84,115,126,146,157,168,188,199,
%T A282147 210,217,219,226,228,233,252,257,259,270,290,301,312,332,343,354,363,
%U A282147 374,385,405,416,427,434,438,445,456,476,487,498,504,507,518,529,549,560
%N A282147 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..k}{(i-j+1)*d_i} = Sum_{i=1..j-1}{(j-i)*d_i}. Case x = 6.
%C A282147 All the palindromic numbers in base 6 with an even number of digits belong to the sequence.
%C A282147 Here the fulcrum is between two digits while in the sequence from A282107 to A282115 is one of the digits.
%C A282147 Numbers with this property in all the bases from 2 to 6 are:
%C A282147 420240, 610273, 848655, 855973, 987751, 1830038, 2347657, 3480366, 3519545, 4832865, 5141958, 6050107, 9010530, 9770426, 11520023, 13951022, 14036167, 14694080, 15106072, 16487203, 24125707, 25209012, ...
%H A282147 Paolo P. Lava, <a href="/A282147/b282147.txt">Table of n, a(n) for n = 1..10000</a>
%e A282147 580 in base 6 is 2404. If we split the number in 24 and 04 we have 4*1 + 2*2 = 8 for the left side and 0*1 + 4*2 = 8 for the right one.
%p A282147 P:=proc(n,h) local a,j,k: a:=convert(n, base, h):
%p A282147 for k from 1 to nops(a)-1 do
%p A282147 if add(a[j]*(k-j+1),j=1..k)=add(a[j]*(j-k),j=k+1..nops(a))
%p A282147 then RETURN(n); break: fi: od: end: seq(P(i,6),i=1..10^3);
%Y A282147 Cf. A282107 - A282115, A282143 - A282146, A282148 - A282151.
%K A282147 nonn,base,easy
%O A282147 1,1
%A A282147 _Paolo P. Lava_, _Giovanni Resta_, Feb 07 2017