OFFSET
1,1
COMMENTS
Here a number is called balanced if the sum of digits weighted by their arithmetic distance from the "center" is zero.
All 1-, 2- or 3-digit balanced numbers are palindromic, therefore all terms are larger than 1000.
The least 1-9 pandigital balanced number seems to be 137986542, but there seems to be no 0-9 pandigital balanced number.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
E. Angelini, Balanced numbers, SeqFan list, Mar 14 2015
EXAMPLE
a(1)=1030 is balanced because 1*3/2 + 0*1/2 = 3*1/2 + 0*3/2.
a(2)=1140 is balanced because 1*3/2 + 1*1/2 = 4*1/2 + 0*3/2.
MAPLE
filter:= proc(n) local L, m;
L:= convert(n, base, 10);
m:= (1+nops(L))/2;
add(L[i]*(i-m), i=1..nops(L))=0 and L <> ListTools:-Reverse(L)
end proc:
select(filter, [$1000..10000]); # Robert Israel, May 29 2018
PROG
(PARI) is(n, b=10, d=digits(n, b), o=(#d+1)/2)=!(vector(#d, i, i-o)*d~)&&d!=Vecrev(d)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Eric Angelini and M. F. Hasler, Mar 14 2015
STATUS
approved