A256076 - OEIS

%I #9 May 29 2018 16:40:28

%S 1823,1933,2141,2251,2633,2963,3061,3391,4091,4253,4363,4583,5393,

%T 5717,5827,6637,6857,6967,7829,8147,8419,8969,9067,9397,14303,14503,

%U 15013,15313,15413,15913,16223,16823,17033,17333,18043,18143,18443,18743,19553,19753,19853

%N Non-palindromic balanced primes.

%C 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.

%C These are the primes in A256075, see there for further information.

%C See A256081 for the binary version and A256090 for the hexadecimal version.

%H Robert Israel, <a href="/A256076/b256076.txt">Table of n, a(n) for n = 1..10000</a>

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

%p filter:= proc(n) local L,m;

%p   L:= convert(n,base,10);

%p   m:= (1+nops(L))/2;

%p add(L[i]*(i-m),i=1..nops(L))=0  and isprime(n) and L <> ListTools:-Reverse(L)

%p end proc:

%p select(filter, [seq(i,i=1001..20000,2)]); # _Robert Israel_, May 29 2018

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

%Y Cf. A256075, A256081, A256090, A002385.

%K nonn,base

%O 1,1

%A _Eric Angelini_ and _M. F. Hasler_, Mar 14 2015