A256090 -id:A256090 - cp's OEIS frontend

A256080 Non-palindromic balanced numbers in base 16.

4144, 4416, 4688, 4866, 4960, 5138, 5232, 5410, 5504, 5635, 5682, 5776, 5907, 5954, 6048, 6179, 6226, 6320, 6404, 6451, 6498, 6592, 6676, 6723, 6770, 6864, 6948, 6995, 7042, 7136, 7173, 7220, 7267, 7314, 7408, 7445, 7492, 7539, 7586, 7717, 7764, 7811, 7858, 7942, 7989

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. Palindromes (A029730) are trivially balanced, therefore they are excluded here.

This is the hexadecimal variant of the decimal version A256075 invented by Eric Angelini. See there, and the base-2 version A256082, for further information and examples.See A256090 for the primes in this sequence.

Cf. A256082 - A256089, A256075, A256076, A256090.

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

A256076 Non-palindromic balanced primes.

Original entry on oeis.org

1823, 1933, 2141, 2251, 2633, 2963, 3061, 3391, 4091, 4253, 4363, 4583, 5393, 5717, 5827, 6637, 6857, 6967, 7829, 8147, 8419, 8969, 9067, 9397, 14303, 14503, 15013, 15313, 15413, 15913, 16223, 16823, 17033, 17333, 18043, 18143, 18443, 18743, 19553, 19753, 19853

Offset: 1

Eric Angelini and 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 (A002385) are "trivially" balanced, so they are excluded here.
These are the primes in A256075, see there for further information.
See A256081 for the binary version and A256090 for the hexadecimal version.

			a(1)=1823 is balanced because 1*3/2 + 8*1/2 = 2*1/2 + 3*3/2.

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

Cf. A256075, A256081, A256090, A002385.

filter:= proc(n) local L,m;
  L:= convert(n,base,10);
  m:= (1+nops(L))/2;
add(L[i]*(i-m),i=1..nops(L))=0  and isprime(n) and L <> ListTools:-Reverse(L)
end proc:
select(filter, [seq(i,i=1001..20000,2)]); # Robert Israel, May 29 2018

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

cp's OEIS Frontend

A256080 Non-palindromic balanced numbers in base 16.

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