A256089 Non-palindromic balanced numbers in base 9.

756, 846, 936, 974, 1026, 1064, 1116, 1154, 1206, 1218, 1244, 1308, 1334, 1398, 1424, 1486, 1512, 1576, 1602, 1666, 1692, 1704, 1756, 1794, 1846, 1884, 1936, 1948, 1974, 2038, 2064, 2128, 2154, 2216, 2242, 2306, 2332, 2396, 2422, 2434, 2486, 2524, 2576, 2614, 2666, 2678, 2704, 2768, 2794, 2858, 2884, 2946, 2972

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. Since palindromes (A029955) are trivially balanced, they are excluded here.

This is the base-9 variant of the decimal version A256075 invented by Eric Angelini. See there, and the base-2 version A256082, for further information and examples.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

filter:= proc(n) local L, m, i;
  L:= convert(n, base, 9);
  m:= (1+nops(L))/2;
add(L[i]*(i-m), i=1..nops(L))=0  and L <> ListTools:-Reverse(L)
end proc:
select(filter, [$1..10000]); # Robert Israel, Nov 04 2024

Prog

(PARI) is(n, b=9, d=digits(n, b), o=(#d+1)/2)=!(vector(#d, i, i-o)*d~)&&d!=Vecrev(d)

Crossrefs

Cf. A256082 - A256088, A256075, A256080, A029955.

Sequence in context: A232341 A261583 A332879 * A252008 A252015 A108374

Adjacent sequences: A256086 A256087 A256088 * A256090 A256091 A256092

Keyword

nonn,base

Author

M. F. Hasler, Mar 14 2015

Status

approved