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%I #15 Dec 27 2019 18:27:10
%S 137,991,1109,1237,1291,1301,1471,1663,1721,1861,1871,7057,7219,7507,
%T 7537,7699,8291,8597,8707,9091,9587,9697,9857,10159,10163,10211,10273,
%U 10321,10627,10631,10739,11027,11437,11551,11777,11887,12239,12401,12659,12671,12821
%N Non-palindromic balanced primes in base 3.
%C A number is called "balanced" here if the sum of digits weighted by their arithmetic distance from the "center" of the number is zero. Palindromic primes (A029971) are "trivially" balanced, so they are excluded here.
%C These are the primes in A256083, respectively the intersection of A000040 and A256083.
%H Thorben Böger, <a href="/A330491/b330491.txt">Table of n, a(n) for n = 1..19999</a>
%e a(7) = 1471 as 1471 is prime and 2000111 in base 3, which is balanced: 3*2 = 1*1 + 2*1 + 3*1.
%o (Python)
%o from primes_file import primes#list containing first 3 million primesfrom baseconvert import base as bdef isbalanced(converted): return sum([(place - (len(converted)/2 - 0.5))*digit for place, digit in enumerate(converted)]) == 0balanced_primes_list = [prime for prime in primes if(b(prime, 10, 3) != b(prime, 10, 3)[::-1] and isbalanced(b(prime, 10, 3)))]
%o (PARI) ok(n)={my(v=digits(n,3)); isprime(n) && !sum(i=1, #v, v[i]*((#v+1)/2-i)) && Vecrev(v)<>v} \\ _Andrew Howroyd_, Dec 23 2019
%Y Cf. A029971, A256083, A256076, A000040.
%K nonn,base
%O 1,1
%A _Thorben Böger_, Dec 16 2019