login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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 * A061327 A023062 A035046

Adjacent sequences:  A256072 A256073 A256074 * A256076 A256077 A256078

KEYWORD

nonn,base

AUTHOR

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

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 20 16:32 EST 2022. Contains 350472 sequences. (Running on oeis4.)