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A256075
Non-palindromic balanced numbers (in base 10).
13
1030, 1140, 1250, 1302, 1360, 1412, 1470, 1522, 1580, 1603, 1632, 1690, 1713, 1742, 1823, 1852, 1904, 1933, 1962, 2031, 2060, 2141, 2170, 2251, 2280, 2303, 2361, 2390, 2413, 2471, 2523, 2581, 2604, 2633, 2691, 2714, 2743, 2824, 2853, 2905, 2934, 2963, 3032, 3061, 3090, 3142, 3171, 3252, 3281, 3304, 3362, 3391, 3414
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
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
Cf. A256076 (primes in this sequence), A256082 - A256089, A256080.
Sequence in context: A250759 A260607 A298910 * A351673 A061327 A023062
KEYWORD
nonn,base
AUTHOR
Eric Angelini and M. F. Hasler, Mar 14 2015
STATUS
approved