A256075 Non-palindromic balanced numbers (in base 10).

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

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

Cf. A256076 (primes in this sequence), A256082 - A256089, A256080.

Sequence in context: A250759 A260607 A298910 * A351673 A061327 A023062

Adjacent sequences: A256072 A256073 A256074 * A256076 A256077 A256078

Keyword

nonn,base

Author

Eric Angelini and M. F. Hasler, Mar 14 2015

Status

approved