A256085 - OEIS

A256085

Non-palindromic balanced numbers in base 5.

140, 170, 202, 232, 266, 296, 328, 358, 392, 422, 454, 484, 518, 548, 635, 660, 685, 710, 735, 765, 790, 815, 840, 865, 877, 895, 902, 920, 927, 945, 952, 970, 977, 995, 1007, 1032, 1057, 1082, 1107, 1128, 1137, 1153, 1162, 1178, 1187, 1203, 1212, 1228, 1237, 1261, 1270, 1286, 1295, 1311, 1320, 1336, 1345, 1361, 1370

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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 (A029952) are trivially balanced, they are excluded here.

This is the base-5 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, 5);

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=5, d=digits(n, b), o=(#d+1)/2)=!(vector(#d, i, i-o)*d~)&&d!=Vecrev(d)

CROSSREFS