Robert Israel, <a href="/A256085/b256085_1.txt">Table of n, a(n) for n = 1..10000</a>

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Robert Israel, <a href="/A256085/b256085_1.txt">Table of n, a(n) for n = 1..10000</a>

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

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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.

Cf. A256082 - A256086, A256077 - A256079, A256075, A256076, A256080, A256081.

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

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

allocated for M. F. Hasler

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

1,1

Here a number is called balanced if the sum of digits weighted by their arithmetic distance from the "center" is zero.

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.

Cf. A256082 - A256086, A256077 - A256079, A256075, A256076, A256080, A256081.

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

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nonn,base,changed

M. F. Hasler, Mar 14 2015

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allocated for M. F. Hasler

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