A256075 -id:A256075 - cp's OEIS frontend

A256087 Non-palindromic balanced numbers in base 7.

364, 420, 476, 492, 532, 548, 604, 640, 660, 708, 728, 764, 820, 836, 876, 892, 948, 984, 1004, 1052, 1072, 1108, 1164, 1180, 1220, 1236, 1292, 1328, 1348, 1396, 1416, 1452, 1508, 1524, 1564, 1580, 1636, 1672, 1692, 1740, 1760, 1796, 1852, 1868, 1908, 1924, 1980

Offset: 1

M. F. Hasler, Mar 14 2015

Here a number is called balanced if the sum of digits weighted by their arithmetic distance from the "center" is zero. Since palindromes (A029954) are trivially balanced, they are excluded here.

This is the base-7 variant of the decimal version A256075 invented by Eric Angelini. See there, and the base-2 version A256082, for further information and examples.

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

Cf. A256082 - A256089, A256075, A256080, A029954.

filter:= proc(n) local L, m,i;
  L:= convert(n, base, 7);
  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

is(n,b=7,d=digits(n,b),o=(#d+1)/2)=!(vector(#d,i,i-o)*d~)&&d!=Vecrev(d)

A256090 Non-palindromic balanced primes in base 16.

Original entry on oeis.org

6451, 7717, 8513, 8963, 9601, 10501, 10867, 11317, 11411, 12227, 13829, 14561, 15461, 15733, 16183, 16529, 16979, 18517, 19333, 19427, 19699, 20149, 20233, 20327, 22483, 22567, 23027, 23561, 23833, 25717, 26083, 26261, 26711, 27077, 27527, 27799, 27893, 28867, 29411, 29683, 30133, 30677, 30949, 31033, 31849

Offset: 1

M. F. Hasler, Mar 14 2015

Here a number is called balanced if the sum of digits weighted by their arithmetic distance from the "center" is zero. Palindromic primes (A029732 in base 16) are trivially balanced, therefore they are excluded here.

These are the primes in A256080. This is the hexadecimal variant of the decimal version A256076 suggested by Eric Angelini.

Cf. A256080, A256076, A256075, A256082 - A256089, A029732.

is(n,b=16,d=digits(n,b),o=(#d+1)/2)=!(vector(#d,i,i-o)*d~)&&d!=Vecrev(d)&&isprime(n)

cp's OEIS Frontend

A256087 Non-palindromic balanced numbers in base 7.

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