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

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

Cf. A256082 - A256089, A256075, A256080, A029952.

Sequence in context: A308617 A353074 A224982 * A054573 A131492 A276026

Adjacent sequences: A256082 A256083 A256084 * A256086 A256087 A256088

Keyword

nonn,base

Author

M. F. Hasler, Mar 14 2015

Status

approved