cp's OEIS Frontend

A282114 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 = 9.

%I A282114 #13 May 30 2019 08:59:23
%S A282114 82,91,100,109,118,127,136,145,154,164,173,182,191,200,209,218,227,
%T A282114 236,246,255,264,273,282,291,300,309,318,328,337,346,355,364,373,382,
%U A282114 391,400,410,419,428,437,446,455,464,473,482,492,501,510,519,528,537,546,555
%N A282114 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 = 9.
%C A282114 All the palindromic numbers in base 9 with an odd number of digits belong to the sequence.
%C A282114 Here the fulcrum is one of the digits while in the sequence from A282143 to A282151 is between two digits.
%C A282114 Numbers with this property in all the bases from 2 to 9 are:
%C A282114 898958160865, 1518029154732,... - _Giovanni Resta_, Feb 13 2017
%H A282114 Paolo P. Lava, <a href="/A282114/b282114.txt">Table of n, a(n) for n = 1..10000</a>
%e A282114 3485 in base 9 is 4702. If j = 3 (digit 7) we have 4*1 = 4 for tyhe left side and 0*1 + 2*2 = 4 for the right one.
%p A282114 P:=proc(n,h) local a,j,k: a:=convert(n, base, h):
%p A282114 for k from 1 to nops(a)-1 do
%p A282114 if add(a[j]*(k-j),j=1..k)=add(a[j]*(j-k),j=k+1..nops(a)) then
%p A282114 RETURN(n); break: fi: od: end: seq(P(i,9),i=1..10^3);
%Y A282114 Cf. A282107 - A282113, A282115.
%K A282114 nonn,base,easy
%O A282114 1,1
%A A282114 _Paolo P. Lava_, Feb 06 2017