A282108 - OEIS

A282108

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 = 3.

%I #11 May 30 2019 08:58:47

%S 10,13,16,20,23,26,29,30,32,35,39,48,55,60,64,69,73,78,82,87,90,91,96,

%T 100,105,112,117,121,130,137,142,144,146,151,155,160,164,165,169,173,

%U 178,180,182,187,192,194,203,207,212,219,224,233,234,242,246,247,256

%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 = 3.

%C All the palindromic numbers in base 3 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="/A282108/b282108.txt">Table of n, a(n) for n = 1..10000</a>

%e 35 in base 3 is 1022. If j = 2 (second 2 from the right) we have 0*1 + 1*2 = 2 for the left side and 2*1 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))

%p then RETURN(n); break: fi: od: end: seq(P(i,3),i=1..10^3);

%Y Cf. A282107, A282109 - A282115.

%K base,nonn,easy

%O 1,1

%A _Paolo P. Lava_, Feb 06 2017